I've also read about complete battalions equipped solely with submachine guns, but I doubt they were Thompsons. While I'm not an expert on the subject either, I'd stick with Russian SMGs, perhaps with the exception of tank crews in American lend-lease vehicles.
Wikipedia's article on the Thompson claims that while the Soviet Union received Thompsons with lend-lease tanks, they weren't issued to the red army because of ammo shortages.
Modern Firearms mentions them being used, but not liked by the Soviets.
While this
page has quite a comprehensive listing of lend-lease shipments, it unfortunately puts all .45 cal SMGs under one listing, "Submachine, Cal. .45, (All Types)", with 137,729 weapons shipped to the USSR.