Agree with usna1985 and (surprisingly) WP.
NAPS is a great opportunity and there's no follow-on obligation to USNA. You're talking about taking a year off before enlisting anyway. Make NAPS that year. NAPS isn't that bad as far as restrictions go. Work out a ton (you'll be surrounded by motivators, priors, and recruited athletes) and do some soul searching. If you decide the officer path isn't for you, then hey, whatever, you gave it a go.
Something else to consider is that they may not be hurting for SEALs right now. It's not like they always need a constant steady flow of dudes to had to BUD/S; it depends on the manning requirements of the Navy. Obviously the Navy and the SEAL program are both very different, but there are actually waiting periods to enlist in the Marine Corps for certain MOSs right now (notably 03XX, infantry). There's the possibility that you could walk into the recruiter's office and be told there's a significant wait before you can ship.
If you're really committed to the SEAL thing, the Naval Academy will hook you up if they decide you're worth it and get selected. Last I heard, no one from my class who graduated and reported to BUD/S had dropped out yet (the overwhelming majority have started training). On average, supposedly Academy guys have something like an 80% success rate at BUD/S.
The SEALs (or, more accurately, the SEAL) on the yard do everything possible to set those guys up for success when they're selected. I know one guy who, before he reported to BUD/S, was attached to the SEAL officer on the yard. His entire job over the summer was working out and prepping for BUD/S. I was talking to his wife the other day and he apparently describes BUD/S as "not that bad," in part because of the training he got at, and after, USNA.