I am not against growing hockey, especially in Tennessee and in Nashville. Let's make that clear. But, there are far better alternatives for accomplishing this.
However, I will play along with what you're getting at.
With enough backing, there is potentially the chance they can get a NCAA team. It would require an insane amount of financial backing on a long term basis. It would never be sustainable. Travel costs, inability to get into a conference, the same things that killed off Alabama-Huntsville. In addition, there is minimal regional recognition, a minimal finances available in the athletic department. So in the best case scenario, you've dumped huge sums of cash which will never be recouped into a program which is likely independent due to geography, noncompetitive due to their inability to get into a conference and because of the inherent travel, a horrible home schedule because of their geography and difficulty attracting opponents. Everything is present in these circumstances to have the venture fail, or at the very least be "not successful," and that is after huge financial investment.
Nashville could build four or five sheets of ice around the metro area instead , start full-fledged youth organizations in each one, provide free equipment for anyone who partakes in their presumably USA Hockey LTS/LTP programs, and have exponentially more people exposed to hockey and the goodwill of the organizations than what is happening with TSU.
Far too many people in the United States have gotten massive hard-ons about NCAA hockey expansion and how it grows the game. NCAA hockey does grow the game, but it isn't a cookie cutter solution suitable for every NHL team and a nearby college athletic program. The Predators organization doing this provides nothing other than temporary good will and provides zero long-term benefits to hockey in Nashville...