For this example we'll assume PHP is installed as a DSO, we're running Apache 1.3.x (since 2.0x may behave quite differently), and using MySQL 3.23.whatever. Consider the request/response process when index.php is requested (the first time):
Apache handles the request by by doing one of two things: passing the request to an available child process or spawning a new child process. This process has many governing factors, but the big one here is a setting (in the httpd.conf file) called 'KeepAliveTimeout'. Depending on how much you've 'fiddled with the knobs', that value (which is a value in seconds) may be anywhere from 5 up to 30, or lower or higher. Most installations of Apache that I've done set a default value of 15, but this value is quite configgerable.
The child Apache process recognizes the file as PHP and shoves it through the PHP interpreter. PHP does its thing, including making any requested database connections. When the Apache child process finishes, the Apache parent process keeps that child process alive for the 'KeepAliveTimeout' value for additional requests from the same host.
If you make a subsequent request to the Apache server before the parent process kills the child process that handled your previous request, and you used pconnect() to attach to the database, you'll save some connection overhead. Otherwise, the benefit of pconnect() is lost.
Bottom line: the right answer depends on your sites traffic, how long Apache keeps child processes laying around for, and a bunch of other stuff (like the MinSpareServers and MaxSpareServers settings in the httpd.conf file), and the number of concurrent connections your database engine will support.
IMHO (and O's are like A's, we've all got 'em), I think it's best to not use pconnect() in most situations, unless you have the ability to fiddle with the knobs on your server config file, your PHP.ini file and your database configuration. I think it's just good programming practice to clean up yer rousources when you're finished with 'em, so the next guy has some system resources to use. Your mileage may vary...