I have one WWII photo of my Dad with a 1911. He was in the supply side of what was then called the Medical Department. He was assigned to Pearl Harbor in the Spring of 1941, was there during the Japanese attack, and was attached to a station hospital throughout the war all the way to the retaking of the Philippines. It was the only firearm he had except during training at Fort Lewis Washington where he had a 1903A3.Generally, anyone whose duties precluded carrying a rifle. The M1 Carbine was specifically developed to replace the M1911A1 and give support personnel something better to fight back with in the event of a Blitzkrieg-style breakthrough of the front lines, but it was soon realized that some things cannot be done when you have to carry a weapon that still requires using both hands. In addition, any GI who badly wanted a .45 eventually found a way to get one, even if they were a rifleman and not normally issued one. I once owned a 1911 that the previous owner won while playing a game of cards with other GIs somewhere in Italy. The poor guy who lost the bet had to report it as a "combat loss" while the new owner was able to sneak it home.
The above and Navy Corpsmen attached to Marine Corps units used 1911A1's or 1911's clear through to the change to plastic, and as I recall I think Army Medic's too. But we were trained in the use of the M14 and later the M16. During my time we only were supposed to carry defensive weapons (Geneva Convention).Military officers, Radiomen, mortar men, Machine gunners, Platoon leaders, Tanker Commanders, Military Police, air crew, pilots,etc.
And AFAIK , there was no 'reporting' of thefts of pistols to any civilian LE agency or database. Theft's were handled within individual units/commands and often NIS.Then as in now, if you wanted a pistol badly enough there were ways to get one. Battlefield pick-ups, bribing those with access to one, and outright theft were among the many means to get your hands on one. A familiar scene from the movie The Thin Red Line was the young Private who badly wanted a pistol, and when he found one carelessly left hanging in its holster next to a bunk he swiped it.