Can I use AirPlay without wifi

You don't need an internet connection to use airplay with local content (i.e. media stored in iTunes/iPhone etc) unless it's protected (i.e. purchased from iTunes) but you do need a wifi LAN setup.

http://support.apple.com/kb/HT4437?viewlocale=en_US&locale=en_US

Yes, you are correct you can not log in via the Apple tv as it doesn't have a browser. Depending on how the network is setup/accessed it may not work regardless, I would talk to the IT dept at the university.