It depends on the school. I would suggest checking with the ROTC program for advice. In most cases a school will be thrilled to get a student who will be a full payer (in the case of a four year Army ROTC winner), but at a school like Yale, that has endowments and other financial resources the decision to chose a student may be less of a financial decision and more of an ideological decision. At Clarkson, I’m going to let admissions know who has an offer, and they are more than likely to be accepted in part because of that offer.