Maybe. I just think if he's offered the Ohio St. job he jumps. As would anyone given the chance to coach the blueblood they grew up cheering for.
Other than the perfectly reasonable assumption that every boy that grows up in Ohio is an Ohio State Football fan, there's little to no public evidence that would suggest he was actually an Ohio State fan. We know know he's a lifelong Browns fan, went to Pitt and then Mt Union, but that's about it. He's never even mentioned it