The military Health Professions Scholarship Program is excellent. I believe Navy commissioned officer nurses are BSNs, and RNs are usually civil service or contract civilians. That's just my knowledge from having a done a temporary stint at a Navy Recruiting District staff and sharing office space with the officers who handled healthcare provider commissioning, recruiting and scholarship programs.
Navy gets its nurses through BSN programs with the HPSP and NROTC slots, as well as direct commission of degreed nurses already practicing. There may well be a USNA grad who, at some point in his or her career, changed lanes and entered Navy nursing, but they likely left active service to return to school and then came back in.
See below link:
http://www.navy.com/navy/careers/healthcare/nurse/
You can click on a "find a recruiter" link to get in touch with the Navy officer in your area who handles health professional scholarship and commissioning programs.
If you continue to review threads on this site, you will see the service academies are generally designed to produce warfare officers for the various service branches and specialties, with health professionals such as doctors and dentists a very small percentage.
All the services have some form of HPSP program. Navy healthcare providers serve the Marine Corps. Googling "health professional scholarships and Army or Air Force" will probably get you there. Ditto for respective ROTC sites for each service. And, don't overlook the USPHS, the U.S. Public Health Service commissioned corps, including nurses in uniform. They serve everywhere. I ran into a USPHS dentist, in Coast Guard uniform, at USMMA at Kings Point. The USPHS commissioned corps is one of the seven uniformed services (but not an armed service), and serve in many different fields all over the world, enjoying many of the same benefits as the other services.
http://www.usphs.gov/profession/nurse/
Good luck!
There usually is a recruiter dedicated to medical recruiting. He/she might have helpful information.