While USNA will accept additional LORs, they generally won't help with one exception.
If his MOC LORs cover a topic that cannot be covered by your son's teachers and BGO, then yes. Examples would be a candidate who works after school, on WEs, and during the summer and thus has no/few ECAs; a candidate whose primary/only ECA is non-school related (e.g., church), etc.
If the LORs simply say your son is a terrific young man who will make a great midshipman, no. The fact they are written by a career Naval officer, someone who used to teach at USNA, etc. won't matter.
Lest you think the above is harsh, here are the reasons. USNA first and foremost cares what the candidate's teachers think. These people typically have known the candidate for at least a year and can comment on his/her academic prowess, leadership in and out of the classroom, etc. The BGO can generally fill in most gaps -- i.e., talk about activities outside of school, etc.
So what good is an extra LOR? If it merely echos the teacher recs in saying how great the candidate it, it doesn't do any good b/c USNA already has that info. If two teachers don't think highly of a candidate, a letter written by a family friend, minister, employer, etc., probably isn't going to counteract the teachers' view. Finally, the teacher recs aren't seen by the candidate (or the BGO for that matter); the ones you sumbit are. Thus, USNA knows you won't sumbit something that isn't glowing -- they're going to defer to the submission that you don't get to read.
I don't want to discourge you and your son from doing everything possible -- but extra LORs almost never are a game-changer.