I don’t have an answer if it will be reimbursable or not as my daughter is not in Navy or at that school, but at three different schools, we have paid a non refundable fee the first year (even for my transfer student at her second school, paid it recently). They ranged between 300- 490. The only one that was ever reimbursed was for my full ride athletic kid, her program paid it after school started as part of her “COA” allowance. My ROTC daughter was not on contract that first semester so I am not sure if it would have been paid, however it did not ever show up on an invoice as part of her school fees and tuition, so I don’t think it would have been submitted for repayment. Another “fee” that wasn’t reimbursable was an $190 “amenities fee” for on campus housing. It shows up on her invoice, however, it is for housing not for cost of education so we pay that every year also.
A good resource at your sons school besides the cadre (he would need to ask the cadre, not you) would be the financial aid counselor at his school that is assigned to ROTC students. That is someone that is totally appropriate for you to contact, though your son may have to do something on his portal showing the school has permission to talk to you, but I still contact this person for my ROTC kid and have used financial aid as a resource for my athletes too. I don’t cross that line and contact any ROTC cadre or civilian employees working with the battalion, nor do I call coaches or compliance for my athletes. But the school knows how they get paid, and in most cases relies on parents to be a part of that, so financial aid can be a good help!