When a hitter gets a single yet advances all the way home on overthrows and there is a runner on base that also scores does the hitter receive any RBI's?

The batter could be credited with an RBI if, in the scorers judgment the base runner would have scored had there not been any overthrows (errors). For example, the batten singles and the runner is on third and scores, then the overthrows occur. The batter is credited with one RBI. In your original question, the batter would, in no case, be credited with an RBI on his own score.