I would say the chances are slim.
The first question you'd have to ask yourself - what level of D3 is he playing at? Strong D3 with pitching in the mid-high 80s consistently or the HS level D3 where you're more likely to see 76 before 86? The top of D3 ball and the bottom are two different worlds.
The next set of hurdles involves sitting out, eligibility/credit transfers, finding an interested team, money, all while going behind your coaches back. His best bet would involve having a trusted, respected baseball guy (former coach, trainer, scout) with connections who can reach out to schools on his behalf discreetly.
What he has going for him is that he is a catcher, they're almost always in demand. That being said, he is hitting .313, not .440. It doesn't sound like he is bored where he is at. Unless he's a top notch lights out defensive catcher I wouldn't worry about it too much unless the move is related to a big academic upgrade. I don't know the situation, but I would not bring it up with the coach unless another school needs an answer.