USNA doesn't care where you apply, whether you are applying to other schools, etc. There's no way they would even know unless you specifically told them. But I can't think of a reason why you would. The only reason I can see it hurting you is telling your BGO in the interview "Yeah USNA is my backup if I don't get into X."
Apply to schools with the mindset you won't get into USNA. Don't just apply to some random backup school. Apply to 3 reaches, 2 matches, and a safety, all of which you'd be willing to attend. Every single one of the schools I'm applying to is on the commonapp with the exception of VMI, Norwich and Penn State. Norwich waived the application fee if I applied by like Aug 12. So that's one application done. Commonapp is very strait forward. Depending on where you are applying there is a supplement essay or two (I only have to do two supplement essays, all of which are 250 words or less). I have been working on a main essay, and am probably 3 weeks away from calling it complete. Go to your counselors NOW to get a recommendation. Give the counselor a deadline as well. Don't say Nov. 1. Or else it won't get done and it'll be put under some filing cabinet. Told my counselor I had a deadline of Aug 31 to get the recommendation done for commonapp. Didn't ask me why it was so early, just said "great I'll have it done by then." Problem is if you wait until october, the counselors are swamped with these. A friend from last year turned her stuff in October for a recommendation to meet a deadline in december. Long story short, the counselor missed all 5 of the college deadlines. When getting my stuff in for USNA, I asked my counselor in April to do the academic and activity information. Guess when it was finally completed? One form in July, other form on the second of August. Told me she'd have it done the week I gave it to her. Use murphy's law. If something can go wrong, it will go wrong. Plan for the worse, and allow a lot of room if something does go wrong.
NROTC will require you to apply to five schools. I applied to 5, plus 2 additional. I just want to have enough options so that it will lessen the blow if I get a TWE from USNA. And remember the end goal isn't getting into USNA, USMA, etc....it's getting the commission. So don't feel that a rejection to USNA is the end of the world.
Good luck!