My experience says you need about 1 to 5 megs per connections depending on what you're doing (that's including the delta increase for both apache and mysql or some other small, lightweight dbms) so this machine probably can't handle all 1000 connections you could generate. 200 to 500 is about the max you could reliably pull from such a box, and you may find that having that many connections open using pconnect may wind up being slower if you're swapping memory instead of just creating/dropping backends as needed.
While some large transactional systems have better performance with lots of persistant connections, mysql type stuff often does better without the headache of persistant connects, and often runs faster due to lower resource usage. Remember, if you leave some memory laying around, apache/php will use it to cache data, as will the file system and the operating system.
