I have a good friend who's a Michigan State alumna and a bunch of friends who went to Georgia Tech, so I have become somewhat of a fan of both teams by proxy. I would describe my interest in both teams as casual -- I watch their games if they don't conflict with the Vols, and I get pissed off when they lose, but I'm always over it within 10 minutes and thinking about something else. If either of those teams were undefeated and had national championship aspirations, and they had to play an 0-8 Tennessee team, I'd root for the Vols to ruin their season without thinking about it. If you're going to have these little side teams, IMO, you've got to be absolutely clear about where your loyalty really lies.
(Note: Michigan State has got to be the most inconsistent, frustrating team in college football to follow. Thank God they're not my real team. My friend basically plans to drink until she passes out every time she watches Sparty play, and after a few years of watching them with her, it's easy to see why.)