As tallwingedgoat said, a variant was still in use in the Vietnam era.
Don't forget that in most armies (except some in the Soviet Union), there always were more rifles (wether bolt-action or semi-automatic) than submachine guns. Even if some men kept using Tommy guns, all the rifles would still have been traded in for M14's or later M16's.
And it wouldn't have ended the outcome of the conflict in any significant way.