definitely
As soon as I found out I'd gotten an appointment to USAFA, I dropped all my other applications, and I didn't take my senior year AP's too seriously.
End of May, I tear a tendon in my foot, report it to DoDMERB, but get my doctor to sign an LoR saying I was fit. A week into BCT, I...
I'm not sure how it is at USMA, but it took my paperwork 3 days to go through at USAFA.
Granted, I was outprocessed for medical turn-back, but the paperwork is all the same. Best of luck.