I can't recall if it's been finalized yet, but there was talk of allowing the COs of NOSCs that aren't on a military base to allow people to go through a PQS and carry a weapon on premises. But in that case, it would be a Navy qualification course to allow the issue of a Navy-owned sidearm, for people who essentially have "security guard" as their collateral duty during the day. Then they check the weapon back in, and go home.
The chances of anyone ever allowing the carry of personally owned sidearms on base are precisely zero.