The rules say the website must be student-designed, built and managed. So does that disqualify teams using phpBB or MediaWiki or even blogging software?
If we use it, can I put up a javascript saying they are about to leave the student-designed portion of the site?
It can be used. I’m not sure how it would be ruled if your entire site was that. 
Most teams have forums on them that are not custom. I’m not sure about the CMS though.
I think there have been threads in the past about that kind of thing…I’m not saying “shut up and search before posting” but you might find some useful information by searching.