I'll disagree with the "focus on your education and don't give a second thought as to the Greek system when choosing a college sentiment". There are thousands of colleges in the US. Greek Life is one aspect of campus culture to consider when looking for the best fit school for you. Of course finding a school that meets your needs academically is important. Think about this for a second. There are many schools that are academically equivalent to UT, but the campus culture at each school is different. That's also a factor when considering a school.
It's hard for me to turn around and say, "Oh don't worry about Greek Life, you're at college to get an education" because my sorority membership is so valuable to me, and I can't imagine my life without Sigma Kappa. I don't think my college freshman self would have had the opportunity to be Greek if I went to the University of Alabama, for example, but there are other aspects of the school that would make it a poor fit as well.
That said, my freshman self would have stood little chance at a school like that because I was uninformed. If I knew about the uphill battle I may face 8 months before recruitment started, I would have had the time to find recs.
So my bottom line for the OP is this:
If you feel that UT is a great fit for you in every other way, and that you won't be emotionally scarred forever on the chance you don't get a bid, send in your deposit. You are fortunate to have discovered GC with plenty of time to learn about UT Recrutiment.
And I will cosign everything that LadyLonghorn and KSUViolet06 said. Great advice.