Somebody probably did this at some point in history. But that said, there would have been several problems with an American using a German weapon (unless really necessary). For one thing the ammunition used by the STG-44 was not supplied by the allies; which would lead to resupply problems. That said, his character probably would have had his issued weapon with him in the tank. I would also think that an experienced soldier would learn to differentiate the sound of allied weapons to enemy ones. The MP-40 was known by GI's as "the burp gun" for example.