I still disagree. I've never seen a study linking a top football program with academic fundraising. To my knowledge, the studies have all refuted any positive link between the two. I agree that football helps some alumni maintain an emotional attachment to the university. I just don't think that translates at all into anything beyond football fundraising, which is a tiny percentage sine overall athletic donations to Ohio State are usually in the 6-8 percent of total donations range. Regardless of football success, the whales are still going to make their eight figure donations to academic colleges and departments as are the lower level President's Club donors. If anything, a rogue program or coach is going to alienate these donors.
To follow your analogy to it's logical conclusion, one would expect peer universities with middling athletic programs to significantly lag Ohio State in fundraising, alumni giving rates and endowment, yet schools such as Washington, Illinois and Minnesota are all equal to Ohio State by each of these measures. Neither Michigan's nor Indiana's private fundraising has been negatively effected by the sharp decline in each of their signature sports, and both exceeded Ohio State's haul last year.