Do only students who are not 3Q'd get consideration for NAPS? You could be considered scholastically qualified because of class rank and GPA. I would think that if you have the "whole" package and are just a little lower than what they like on the SAT they could give the NAPS apt.
Generally speaking, the candidates sent to NAPS are sent there for
academic reasons - either to boost their SAT/ACT scores, get more academic exposure, or to take courses that they need (i.e. Chemistry, Physics, Calculus), but didn't take during their high school years. It's never because they need to get a better CFA score or to work on their "leadership" skills.
Sometimes, those from the fleet are sent to NAPS simply because they have not been exposed to academics in so long. They are being brought up to speed even though their high school credentials were outstanding - yet a bit dated. For instance, maybe they've been out of high school for 3 years and have not even seen a Chemistry or math book during those years.
However, to a large degree, most of the NAPS students are being recruited for some sport. Not all - but most.
It is very rare that anybody is sent to NAPS if they are 3Q'd. Why would they go to a preparatory school if they need no preparation?
It is extremely rare for a 3Q'd candidate, who is not offered an appointment, to be offered NAPS. The academy's position is: If a candidate really wants to attend USNA and did not receive an appointment, they can apply
again - just like the NAPS students have to do.