It helps somewhat. Here's how:
(Assuming a competitive nom slate), each candidate first competes against his/her slate for an appointment. If he/she doesn't receive that MOC appointment, he/she goes to the national pool. Obviously, if you are on 3 slates, that gives you three shots to "win" your slate before going to the national pool.
Ditto for a Pres nom . . . you compete against the other Pres nominees for one of the 100 appointments before going to that national pool.
Thus, with four noms, you get four shots vs. a lesser number with fewer noms.
The above said, one is often enough, especially for candidates in super-competitive areas. The reason is that, although they may only get one nom (b/c MOCs get together to limit the number any one candidate receives) and may not win his/her slate, when that candidate goes into the national pool, he/she is extremely competitive and may well get one of the "at large" slots.
It is important to understand that, at least for USNA and I assume for the other SAs, you do NOT get "bonus points" or something similar from an admissions standpoint for obtaining more than one nom. The reason, as discussed above, is that some candidates have no hope of getting >1 b/c of the way MOCs in their area parcel out noms. That's something beyond the candidate's control and so candidates are not "rewarded" or "punished" for the number of noms they receive.