Echo 'Hoops +1 , and will go a bit further -- I have never heard of anyone who successfully completes NAPS not get offered an Appointment.
First, NAPSters are required to apply for all Nominations that they are eligible for -- Admissions first choice is to use those Noms. However, on top of that, Admissions can draw on the SECNAV pool). Bottom line, they will find a way to get successful NAPSters in.
Key there is "successful." NAPS can be a tough program for some, and in my day there was a fair amount of academic attrition as well as a handful of honor cases. In addition, I would expect that USNA could always deny admission for conduct or aptitude issues that fall short of disenrollment. Again, the bottom line and good gouge is that a NAPs candidate will be admitted unless they fail out, or do something stupid.