well... as you know Yale denies admission to 13 applicants for every one it approves. If you take out the athletic and ethnic hooks, its more like 17 denials for every unhooked applicant it admits.
So... work YOUR hook, which is NROTC. If you're hooked, the odds go up to at least 1 in 4.
Now, look at this from the perspective of the Yale admissions committee. Of the 30,000 or so applicants, about 27,000 will have SAT over 2100, several very strong ECs, and GPA above 3.8 unweighted with a good % of those classes being AP, IB or Honors. So, exactly HOW do the adcoms pick the one in 17 unhooked?
The point is, emphasize what is really unusual about you, which is your desire to serve as a Naval Officer. You will add a spice, a flavor, a perspective that the vast majority of applicants will not possess. Your NROTC participation, along with your Legacy status, will go a long way toward differentiating you. So, work the NROTC angle for all its worth. Ride it hard and put it away wet. Have no shame.
Oh, and as to the NROTC scholarship, I'm certain that NETC would approve many, many more scholarships for use at Yale than it has applicants who have been accepted into Yale (or H). Get into Yale, and the good folks at NETC will soon treat you like a best friend.