I live in Knoxville; and while I have seen a few homeless people downtown (usually the same ones time and again), I think that it is a different matter around campus – really nothing that I have seen in and around campus.
I agree with @tsbna44 when he and others suggest that you visit both campuses – and specifically the engineering facilities – perhaps on admitted students days at the respective campuses. UT has been spending a lot of money on its engineering facilities in the recent past (Engineering Buildings - Tickle College of Engineering), so there have been some significant upgrades there, in addition to lots of money being raised for engineering programs. I also agree with the posters who suggest that you shouldn’t have any trouble avoiding other students from your high school at UT.
And, UT has beaten Alabama 2 out of the last 3 years in football. 