Imtrouble,
it depends on how motivated you are for a Navy flying lifestyle - it is unusual but not silly to apply for both. If you really want to join up, my advice is to put all your efforts into getting to FSP first, and make sure the recruiters know it. This also demonstrates motivation to fly. Most other applicants will opt for Observer as second flying preference - you should seriously consider this on your application - Observer is a very challenging front seat role in the Navy (they need to have basic helo flying skills also)- the various selection boards may think twice if you have the option to jump back into the "easy option" of nursing when the mil training gets tough.
That said, if the training pipe is blocked up for a year or so (typical) the opportunity to get into Navy nursing and keep applying would be reasonable. Military nursing is not like the civil world - you are mainly dealing with healthy people!
Consider that right now the only real impediment to you being selected for FSP is your performance and profile in the selection process. You will only get one shot at FSP (unless you get sick / family crisis or similar). If you join the Navy as a nurse, the Navy's desire to release you could become an additional impediment on top - the need for nurses could affect your application and your bosses could have an + or - influence on your application. Yet another reason to keep pushing for option A.
RM