If your son already has an account with NFCU, there are other locations around Annapolis easier if you don't want to go onto the Yard.
Bancroft Hall: just off Mid Store parking lot near the archway from that lot into area adjacent to McDonough Hall
Naval Support Activity Annapolis: The Navy Exchange and Commissary are in a no-gate part of the base, and there is a NFCU branch office there. Drive over Naval Academy Bridge, take immediate right onto Rt 648, Baltimore-Annapolis Rd., but veer right onto Greenbury Point Rd very briefly. You should see the sign for the Naval Support Activity, and take the right-hand fork of the road, NEX/Commissary complex are on the right. If you find yourself at the golf course, you've gone too far on Greenbury Point - but take the scenic tour and check out the Brigade Sports Complex. Backtrack to the light and take the other branch.
Main NFCU branch for Annapolis: in a building near Annapolis Mall. If you can find Modell's Sporting Good store in the same shopping center adjacent to the Nordstrom's end of the Mall complex, with a Marshall's, Trader Joe's, etc., the NFCU is on the ground floor of a nearby office building adjacent to Jennifer Rd.
If your son doesn't have his account open yet, and that will happen on I-Day during his in-processing, not sure if you can deposit now. You can always ask.