(I have tested both TCP/IP and named pipes, both fail. This is from my named pipe test)

C:\mysql_5.1.49\bin>mysql -u root -W
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 1
Server version: 5.1.49-enterprise-gpl-advanced MySQL Enterprise Server - Advanced Edition (GPL)

Copyright (c) 2000, 2010, Oracle and/or its affiliates. All rights reserved.
This software comes with ABSOLUTELY NO WARRANTY. This is free software,
and you are welcome to modify and redistribute it under the GPL v2 license

Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.

mysql>status
--------------
mysql  Ver 14.14 Distrib 5.1.49, for Win32 (ia32)

Connection id:          1
Current database:
Current user:           root@localhost
SSL:                    Not in use
Using delimiter:        ;
Server version:         5.1.49-enterprise-gpl-advanced MySQL Enterprise Server - Advanced Edition (GPL)
Protocol version:       10
Connection:             Named pipe: MySQL
Server characterset:    latin1
Db     characterset:    latin1
Client characterset:    latin1
Conn.  characterset:    latin1
UNIX socket:            MySQL
Uptime:                 21 sec

Threads: 1  Questions: 4  Slow queries: 0  Opens: 15  Flush tables: 1  Open tables: 8  Queries per second avg: 0.190
--------------

mysql>set GLOBAL max_allowed_packet=2048;
Query OK, 0 rows affected (0.00 sec)

mysql>show global variables like 'max%';
+----------------------------+----------------------+
| Variable_name              | Value                |
+----------------------------+----------------------+
| max_allowed_packet         | 2048                 |
| max_binlog_cache_size      | 4294963200           |
| max_binlog_size            | 1073741824           |
| max_connect_errors         | 10                   |
| max_connections            | 151                  |
| max_delayed_threads        | 20                   |
| max_error_count            | 64                   |
| max_heap_table_size        | 16777216             |
| max_insert_delayed_threads | 20                   |
| max_join_size              | 18446744073709551615 |
| max_length_for_sort_data   | 1024                 |
| max_prepared_stmt_count    | 16382                |
| max_relay_log_size         | 0                    |
| max_seeks_for_key          | 4294967295           |
| max_sort_length            | 1024                 |
| max_sp_recursion_depth     | 0                    |
| max_tmp_tables             | 32                   |
| max_user_connections       | 0                    |
| max_write_lock_count       | 4294967295           |
+----------------------------+----------------------+
19 rows in set (0.00 sec)

mysql>show session variables like 'max%';
+----------------------------+----------------------+
| Variable_name              | Value                |
+----------------------------+----------------------+
| max_allowed_packet         | 1048576              |
| max_binlog_cache_size      | 4294963200           |
| max_binlog_size            | 1073741824           |
| max_connect_errors         | 10                   |
| max_connections            | 151                  |
| max_delayed_threads        | 20                   |
| max_error_count            | 64                   |
| max_heap_table_size        | 16777216             |
| max_insert_delayed_threads | 20                   |
| max_join_size              | 18446744073709551615 |
| max_length_for_sort_data   | 1024                 |
| max_prepared_stmt_count    | 16382                |
| max_relay_log_size         | 0                    |
| max_seeks_for_key          | 4294967295           |
| max_sort_length            | 1024                 |
| max_sp_recursion_depth     | 0                    |
| max_tmp_tables             | 32                   |
| max_user_connections       | 0                    |
| max_write_lock_count       | 4294967295           |
+----------------------------+----------------------+
19 rows in set (0.00 sec)

mysql>connect
Connection id:    2
Current database: *** NONE ***

mysql>show session variables like 'max%';
+----------------------------+----------------------+
| Variable_name              | Value                |
+----------------------------+----------------------+
| max_allowed_packet         | 2048                 |
| max_binlog_cache_size      | 4294963200           |
| max_binlog_size            | 1073741824           |
| max_connect_errors         | 10                   |
| max_connections            | 151                  |
| max_delayed_threads        | 20                   |
| max_error_count            | 64                   |
| max_heap_table_size        | 16777216             |
| max_insert_delayed_threads | 20                   |
| max_join_size              | 18446744073709551615 |
| max_length_for_sort_data   | 1024                 |
| max_prepared_stmt_count    | 16382                |
| max_relay_log_size         | 0                    |
| max_seeks_for_key          | 4294967295           |
| max_sort_length            | 1024                 |
| max_sp_recursion_depth     | 0                    |
| max_tmp_tables             | 32                   |
| max_user_connections       | 0                    |
| max_write_lock_count       | 4294967295           |
+----------------------------+----------------------+
19 rows in set (0.00 sec)

mysql>create database mytest;
Query OK, 1 row affected (0.00 sec)

mysql>use mytest;
Database changed

mysql>create table test (t mediumtext);
Query OK, 0 rows affected (0.02 sec)

mysql>insert into test values ('123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890');
Query OK, 1 row affected (0.02 sec)

mysql>select length(t) from test;
+-----------+
| length(t) |
+-----------+
|      6000 |
+-----------+
1 rows in set (0.00 sec)

Clearly the INSERT command was much larger than the max_allowed_packet setting. This INSERT should have failed.