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Id love to earn the masters on the navy's time, but Im not sure I can get on the books without the masters or some decent flight hours. Also, I could finish the masters program at my school in under 2 years.
Apply to the navy and grad school. you have nothing to lose. If you get into both, then you make the call, otherwise take what you get. you should be able to get your MS in two years if you are on top of things, maybe even one if you kick ass and don't have to write a thesis (Coursework only MS are available at a lot of universities). Open as many doors as you can at once, then pick the best option.