Depending on how this network is set up and how internet access is provided to the various computers, there's a few things to take note of here:
1) Port blocking. Not good enough today unfortunately, most P2P programs just open copious ports until they find one that they can use. At least one (the infamous Kazaa and maybe others) will use Port 80 which you cannot block if you want internet access.
2) Firewalls. Software firewalls are easily disabled, bypassed or generally broken. A hardware firewall is more effective but not all of these offer the facility to filter types of traffic plus of course some P2P programs emulate web browser activity exactly which'll bypass any hardware filter.
3) Users. In this day and age where most homes have at least two or three computers due to costs falling through the floor, its never been easier to have a home network. And herein lies the problem. If the users have their own networks at home (which are basically just cut-down versions of the one you have at the school), they'll know all the tricks used to restrict access and make appropriate changes.
4) In conjunction with number 2 above, it may be possible either accidentally or intentionally to disable the monitoring software.
A step in the right direction however is to basically block the sites on each individual computer by adding a whole bunch of p2p download sites to each system's HOSTS file (see http://spyware-remov...e-remover.shtml
and the "Override Your Hosts File" section).
Another step in the right direction is to use Limited Accounts as opposed to administrator accounts which will often prevent installation of most things including these types of programs.
Of course it could be prudulent to step up active physical monitoring of the systems, though this of course is most likely cost prohibitive.
Just some food for thought.