That might be ok. A football player can be drafted in the MLB draft and keep the signing bonus and then play football.
You can't receive money for a sport you will play in college and you can't receive endorsement money. Signing a contract for another sport would usually be ok. Such as playing baseball professionally doesn't preclude you from being on scholarship for football.
Is it limited to the big 4 leagues, because it seems like a loophole could be found with that. What if a billionaire alum from x-university owns a semi-pro hockey team, and "signs" multiple football prospects to a "contract" that has a signing bonus of say, $25 k, and they don't end up playing hockey for obvious reasons, but keep the bonus?