Unusual Eligibility Question

I don't see where it would anywhere as long as everything is paid for by the player.

As long as you don't get paid for playing BB you are still good. They can even reimburse you for travel and room as long as it is reasonable.
Some senior teams here are loaded with college players and at least 1 of they pays all expenses.
My son threw bull pen for a pro team under Ron Davis and it raised some questions but he never played for them so he was okay.