1000% with clarkson...it depends! I also agree with k2rider, there are thousands of kids that apply for a scholarship, and in the end cadets on scholarship are in the minority.
Our DS was AFROTC, he never finished his application to NYU Sterns and never applied to UNCCH (NC resident), however, after he was awarded the scholarship, he received acceptance letters to both. I actually thought it was some sort of scam, like wanting me to pay money to get him in. I called admissions and they said indeed he was offered a slot because at both of these schools the AFROTC unit sat on the admissions board. The AFROTC unit knew he had the scholarship and was able to see his stats, thus they put him up for admissions. It does happen, but as others have stated it depends on the school.