I don’t believe so. This close to DC and the “big” Navy Ball and the “big” MC Ball, military folks may choose to go into DC to that one. Those balls tend to be held near large installations with multiple commands. USNA and the Naval Support Activity are relatively small installations and would usually not have one on their own. Those things tend to be pricey, with ticket prices linked to paygrade. Decades ago, in the days of calling cards on silver salvers in a home’s foyer, official calls made and returned, mandatory social events, hand-written invitations on officer crest stationery, and more, it was pretty much expected the officers from a command would go to any nearby Navy Ball. Even 20 years ago, it was like pulling teeth to fill a table. People would rather do other things than pay for a banquet chicken dinner, pricey drinks, child care and no way to satisfy a wide variety of dancing and musical tastes. I would bet mids wouldn’t be at all pleased to swap weekend liberty for another draft on their midshipman pay for “mandatory fun.”
I and DH usually went and donated extra money so junior sailors and their guests could go, out of a sense of duty. I suspect some hosted seats are made available for mids at the DC Balls, but not a big deal.