I agree re getting your USNA packet in early -- it can always be supplemented and there is a process for doing it. Also, the Admissions Board operates on a rolling basis (different from appointments necessarily being rolling) so early is good.
Each MOC has his/her own process which is in parallel to -- but not directly connected with -- the USNA admissions process. In my experience, the nominating admin person collects all of the packets. Once the deadline has passed, they are provided to the nominating committee (the volunteer citizens) to review. I suppose there is some marginal benefit in getting a packet in early IF they note when the packet was submitted. When I served on such a committee years ago, that wasn't something we considered. I think USNA says that just to encourage folks to get it done -- not b/c they actually know earlier is better with MOCs.
If you can add to the MOC packets, then submitting early is fine. But I've not yet seen an MOC who makes the decision before his/her self-imposed deadline, so you do have the time you're given.