Whether or not a school gets a P5 invite or not isn't about football. If it was, Rutgers would still be in the AAC. It's about media markets and demographics. You must have a football team, but if the numbers work, you're in the running.
Boston College got into P5 with a mediocre football team in 2004. It's a hockey school, so even men's BB was a minor factor. They apparently had no problem with adding a New England market, and later on they added Syracuse, certainly not because of the football team, which was pathetic at the time, but because of history and tradition. They have a big fanbase that supports the school because there's nothing comparable anywhere around them.
We are the same. As the flagship state U in CT, we have no competition within the state. There's no Connecticut State U, or Connecticut A&M. We're the only game in town. It worked for Syracuse and even for BC. There's no reason we couldn't do it, except that our university administration was clueless and totally incompetent.