It's a nice thought, but that's not really the way it works. Each opening for the Academy can have up to 10 nominations so having a person with an LOA has no real effect on it since one of the other 9 will then get the appointment. If you move the LOA winner out of the mix the next person in line may move up onto the slate, but since they were the 10th choice their chance of an appointment are very, very slim. I would argue the opposite, and that only applying for one nomination could possibly keep another deserving person out. When my son got his LOA to USAFA he applied to both senators and our representative. He was put on all three slates, and even after he accepted his appointment his nomination source was moved amongst all three MOCs until the final class was put together. It is like a big jigsaw puzzle, and the more sources that the board has to move your appointment around to, the more chance they have to build a class of the most deserving candidates.
I agree with Stealth....
This is similar to our DD's experience. Our DD was a recruited athlete and applied to both Senators and our State Rep. She had received calls from all 3 MOC's saying that she'd receive a nomination from each of them. Her nomination source shifted from one to another until they determined who "claimed" her. Good thing for her as a blue chip recruit was that she could have received the Supt's nomination had none of them nominated her.
I'd suggest to apply to all nominating sources. It only takes 1 nomination.
IMO, the perspective candidate(s) must do all they can do to secure a nomination(s). They've put in a lot of energy to get to the point....don't back off now! Worrying about taking another persons possible nomination should not be the reason you do not go after all nominating sources.