We met a family during I-Day. We shared different floors of a duplex, so got to talk a few times. The parents said that their son was admitted last year to USNA, but the coach told him he could go to NAPS if he chose to gain an extra year of experience. The Plebe had several teammate friends that were going to NAPS, so he decided to do the same. Of course they could have been BS'ing with me, but if true, this story did bother me.
A NY Times article gave this number: "...… of the 300 students in the 2011 class of the Naval Academy Prep School, 110 are recruited athletes — typical for the other service academies." Seems low. I'm not that familiar with Navy's prep school, but I've seen other estimates of 40% - 50% for USMAPS.
USMAPS is open to all candidates that were found academically unqualified during the admissions process to USMA. There is no separate application process. With the limited number of spaces almost all selected for USMAPS will be recruited athletes, enlisted soldiers, and minorities who can fulfill diversity goals. If a candidate wants to be considered they should talk to their RC.
On all USMA NCAA rosters there are 185 players that attended USMAPS for all class years - averages about 47 per class year. Since USMAPS enrollment is about 250, the percentage of athletes is well below 50% even accounting for attrition.
The demographics of athletes at USMA, USNA, and USAFA are similar. Some of the athletes are outstanding students and some are well below the norm. No college can compete at the D-1 level without sacrificing academic standards.
Since many USMAPS athletes played 4 years of varsity sports at USMA, I'd say yes.
While I'm not familiar enough with NCAA regulations to provide an authoritative answer, my guess is that because the academy prep schools are not colleges, sports played there do not count against NCAA eligibility.