I'd actually be open to that, if it was a combat related career path. I'm not much interested in anything like logistics or supply.
I dont think you have much to worry about regarding USNA. I know several people who applied, or were asked to apply to USNA that were prior enlisted. USNA sets aside several spots for prior enlisted folks, and while its not a sure shot, several folks I know were essentially told "if you apply, and you aren't a dirt bag, you're getting picked up."