I don't think having a good college football team 'hurts' a college academically, it likely helps it. But from a GT perspective it doesn't really need any 'help' attracting students.
It's become a very difficult school to get into and has way more applicants than spots. GT has changed admission policies radically since the time I was in school. It has gone from allowing alot in and then having a high percentage fail out to allowing a much more select group in, but having alot fewer dropouts.
On another item, and this may not be the best place for it, but here is an article from Dennis Dodd and the ACC being opposed to college expansion. According to the article the ACC FB coaches were unanimous in opposing college expansion before 2025. They feel there are other issues that need to be fixed (including NIL and the transfer portal) before expansion is pursued. From the article it also sounds like the B10 is a 'no' right now on expansion.
B12, PAC12 and SEC are in favor, though SEC is saying they are also fine keeping as it is right now.
ACC coaches and officials want other problems solved before tackling potential CFP expansion
www.cbssports.com
Expansion is very likely to happen, but the odds of it happening before 2025 are going down significantly. It also appears at least a couple of conferences (including the ACC) are intent on going to 2025 and then allowing a bidding war and splitting the CFP package up amongst multiple media entities. IMO I don't think some of the conferences want so much power resting with ESPN.