The fact that Derek Dooley finished in the top 25 in recruiting every year without actually recruiting tells you all you need to know about Tennessee football, tradition, and facilities.
Tennessee's facilities are among the nicest, but not the most expensive. Of course, Nike's founder has dropped so much money in Oregon's training facility, it boggles the mind. Here is a site I found interesting.
However, much of it is not just spending the bucks. A part money can't buy is doing it smarter. What is going to make ATC even nicer is when the athletic dorm and parking garage are completed. Add that the Thornton center is in that general vicinity, and the football team will be parking their cars, living, training, and getting help with their studies in a smaller area than most of the competition.
And once that is in place and the recruits can see that, I feel that big convenience will not go unnoticed as they visit different schools.
I find it interesting the Nike swoosh has equal branding prominence as the Power T on the opening segment. I wonder what that's worth... hopefully Tennessee is getting some $$$s from that relationship to help fund these facilities.
To specifically answer your question, I don't think any recruit would be unimpressed with the sheer awesomeness of our facilities. We are on par with the elite in those regards.