It is not necessary to have a nom to be accepted to NAPS. In fact, to the best of my knowledge, having or not having a nom isn't a factor in the decision. In the past, the candidates I've had go to NAPS have not had noms, but I've only had a handful over the years.
I got a conditional offer pending medical waiver to NAPS last saturday without a nom...but im a recruited athlete....but my good friend received an appointment to NAPS without a nom too since its very difficult to compete for noms in a large navy town like San Diego
I recently received notification of my acceptance to NAPS for the class of 2012 and I don't have a nomination. If you have a competitive profile but no nomination, I think that NAPS is a viable option. Good luck!