Here's my fifty cents. The Class of 2009, the current plebe class, roughly 7% of them are prior enlisted, and 20% of that 7% went to nuke school. Also 65% of the 7% went to NAPS, Naval Academy Prepatory School. Those are just facts and figures to ponder.
If you get accepted to either Academy, and you truly desire to become an officer do as Nike says: just do it. You will have to put up with some BS, but it will be worth it in the end. If you have more questions about the Naval Academy, my roommate and I would be happy to talk to you. Neither of us are prior enlisted, but we have a few in company who we could get information from about their experiences, as well as a bunch of NAPSters.
ADH
USNA '07
Yes, I do realize I am not an officer yet; just a lowly midshipman.