Possibly, but that’s money the school does not have to solicit. Whether it goes through the AD or athletic department or football team directly is semantics.
It is not a coincidence that of the three public P5 teams in Texas, the two PUF schools (UT and A&M) are making money hand over fist and TxTech is barely breaking even, as I have read recently. All get P5 money, donations, fill stadiums etc.
Can’t argue that the PUF is not a massive advantage. Add 20+yrs of P5 money and it is not a great mystery. UH would be completely accelerated in its athletic and academic endeavors with a share of the PUF and P5 money.