Yes, nothing is stopping cadets from starting a club. I would venture to say that all non-mainstream clubs were made by a cadet. The hard part would be getting funding from DCA but if you just want a group of cadets with similar interests and are willing to take care of your own funding then it should be easy.
Haha I was wondering this same thing... I love my guitar, and that's something I don't want to leave behind!
I hope that there are opportunities to be in bands and such, just as there would be at regular colleges... not necessarily school-oriented in any way, but just jamming with friends.
I think there's a Jazz club here...other than that I haven't really seen or heard cadet run bands. Probably cuz there really is no place to actually play. I wondered about the same thing before I came here, but it probably really is only because there simply isn't anywhere to play without pissing people off. Maybe cadets play off-post?