I checked the mysql.user table and it doesn't look like there is a setting there for it:
+-----------------------+-----------------------------------+------+-----+---------+-------+
| Field | Type | Null | Key | Default | Extra |
+-----------------------+-----------------------------------+------+-----+---------+-------+
| Host | char(60) | NO | PRI | | |
| User | char(16) | NO | PRI | | |
| Password | char(41) | NO | | | |
| Select_priv | enum('N','Y') | NO | | N | |
| Insert_priv | enum('N','Y') | NO | | N | |
| Update_priv | enum('N','Y') | NO | | N | |
| Delete_priv | enum('N','Y') | NO | | N | |
| Create_priv | enum('N','Y') | NO | | N | |
| Drop_priv | enum('N','Y') | NO | | N | |
| Reload_priv | enum('N','Y') | NO | | N | |
| Shutdown_priv | enum('N','Y') | NO | | N | |
| Process_priv | enum('N','Y') | NO | | N | |
| File_priv | enum('N','Y') | NO | | N | |
| Grant_priv | enum('N','Y') | NO | | N | |
| References_priv | enum('N','Y') | NO | | N | |
| Index_priv | enum('N','Y') | NO | | N | |
| Alter_priv | enum('N','Y') | NO | | N | |
| Show_db_priv | enum('N','Y') | NO | | N | |
| Super_priv | enum('N','Y') | NO | | N | |
| Create_tmp_table_priv | enum('N','Y') | NO | | N | |
| Lock_tables_priv | enum('N','Y') | NO | | N | |
| Execute_priv | enum('N','Y') | NO | | N | |
| Repl_slave_priv | enum('N','Y') | NO | | N | |
| Repl_client_priv | enum('N','Y') | NO | | N | |
| Create_view_priv | enum('N','Y') | NO | | N | |
| Show_view_priv | enum('N','Y') | NO | | N | |
| Create_routine_priv | enum('N','Y') | NO | | N | |
| Alter_routine_priv | enum('N','Y') | NO | | N | |
| Create_user_priv | enum('N','Y') | NO | | N | |
| ssl_type | enum('','ANY','X509','SPECIFIED') | NO | | | |
| ssl_cipher | blob | NO | | | |
| x509_issuer | blob | NO | | | |
| x509_subject | blob | NO | | | |
| max_questions | int(11) unsigned | NO | | 0 | |
| max_updates | int(11) unsigned | NO | | 0 | |
| max_connections | int(11) unsigned | NO | | 0 | |
| max_user_connections | int(11) unsigned | NO | | 0 | |
+-----------------------+-----------------------------------+------+-----+---------+-------+
37 rows in set (0.00 sec)
Depending on whether you're using MySQLi or PDO, your PHP MySQL connections should either hang up when the request does, or be shared in a pool for the Apache process.
For example, with PDO, to turn off persistent connections (I think this is the default), connect to your DB with:
$pdo = new PDO($dsn, $user, $pass, Array(PDO::ATTR_PERSISTENT => false));
If you want your scripts to use persistent connections, but you have too many connections open to your database in sleep mode, you should think about configuring your Apache's MaxServers, MaxSpareServers, MinSpareServers and StartServers so that not so many hang around when they aren't needed.