Not completing the FAFSA will not hurt anyone's chances for an appointment, just as it would not hurt anyone's chances for admission to a civilian university. I'm not sure if that is your specific question. Perhaps your question is whether there are any education-related expenses associated with attending USNA that would be covered by the loans or grants that require FAFSA? I suspect the out-of-pocket expense of going to Annapolis is small enough to warrant skipping FAFSA for most people. Other than Plan Bs and Cs. In our case Plan C is not being able to follow through with USNA ("A") or a 4-year NROTC scholarship ("B").
FAFSA is an interesting process. I went through it with my daughter a few years ago. Needless to say, their interpretation of my wealth is a lot different than mine.