Couple of things. In Germany when we had "Lariat Advances"* every unit kept a portion (1-3 days, IIRC) of their basic load in their arms rooms fro when we practiced rolling to the border. Tanks had a full combat load on them in the motorpools, that's why Armor battalion Motor Pool guards were issued three live rounds.
Sidearms and ammo to each E-? and above. As long you DO NOT have to draw them in the morning and turn them in each evening, fine. Otherwise the CQ (and a runner, two man rule in the arms room) will simply be permanent armorer after say 4pm. Also, not many units have "Sidearm, one each" on their MTOE for most enlisted. Pretty much every "E" up to E-8 in the Army has M4/M16/M203/M240/M2 as their personal weapon. Only 11C's (Mortarman), 31B (Military Police), and 56M (Chaplin's Assistant) have sidearms as their issue weapons. There might be a couple of others, but not many.
And yes, weapons immersion works. The ONLY AD we had in my MP company in 4 years I was there, an E-7 PSG. The E-1's through 6's did weapon draw turn-in 3x per day. They were used to drawing, loading and unloading their sidearms. The SFC, not so much. Maybe only when he did MPDO, and even then, some/most did not draw their weapons (Stupid, but I digress). He had to because we were so short NCO"s that we had to us Platoon Sergeants as Shift Supervisors. Having not done it much, at the end of his shift he killed the clearing barrel. Not once, but twice. Yeah, that stirred up a stit shorm. The USAREUR, Corps and Division PM all got their panties in a knot. It would have been less bad had he shot someone.
Some hurdles, but could be done.
But keep in mind, not many people in the Army/military are gun people.