It is very clear that USNA will not admit candidates from another Service Academy , and vice versa, for the "poaching" purposes described above. NAPS may be different, but the considerations are the same. I would never counsel a candidate to attend NAPS with the intent of applying to another Service Academy , or if their true goal was attending another Service Academy. However, OP already made the decision to attend NAPS, so the question is 1) whether he can apply to West Point while attending NAPS, 2) would West Point consider admitting him, and 3) if he applies and is accepted, will Navy release him.
First, with respect to 1) and 3), NAPsters enlist in the Navy, so OP should look at the terms of his enlistment contract to ensure that he can leave the Navy if accepted to USMA. It is my understanding that persons who enlist for NAPS can drop out, but I don't know if there is some tail Reserve committment. If a NAPSter is able to drop out at anytime, I wouldn't see any impediment to applying for West Point, and attending if admitted. That would explain the comment above seeing someone apply for nominations to multiple service academies from NAPS.
I think the bigger question is 2) -- whether USMA would consider admitting someone from NAPS. While I get the comment about commitment going both ways, there are other factors involved. First, Navy is investing in a candidate from the minute they start NAPS (and Army is investing in their MAPS candidates). Second, while USNA is not committing to the NAPS candidate , it is as close to a sure thing as you can get -- as long as you successfully complete the program , USNA will find a spot for you. (As an aside, is a person who doesn't sucessfully complete NAPS really competitive to attend USMA ?). I don't think OP mentioned being a recruited athlete, but if thats the case, it adds additional candidates
All in all, I would expect USMA to be extremely reluctant to accept a NAPSter, but would suggest that OP talk to his WP Field Force Rep to run the question up the West Point flagpole. If West Point is willing to consider the application, then I would recommend talking to his chain of command at NAPS, and let them know that he is still interested in attending USMA without burning bridges with USNA. The chain of command is going to find out sometime (I would suspect that USMA would at least want a recommendation from NAPS), so OP would be better off being upfront and getting support early than springing a surprise on NAPS leadership later.
As a final note, while the Army /Navy rivalry is strong, this is really an issue of inter-collegiate ethics and what is best for the services, not USNA Admission's desire to BEAT ARMY. USNA Admissions and most BGO's really don't look at West Point as "competition". We all know that candidates often apply to multiple Service Academies, and while I will make a point to explain the differences and advantages of USNA over USMA, I never try to discourage a candidate from choosing the Service Academy that is right for him/her. Except for a certain Saturday in December, we are all on the same team.