Yes, thats correct. There is a gasket that is supposed to seal the overflow drain fitting against the back of tub. The leak that you are talking about does happen occasionally altho not real often in my experience.. More common would be the tub boot (the drain in the tub) itself, or the valve leaking. But the overflow gasket could be the source of your problem.
You could test the theory by pouring water directly over the overflow plate but not letting any of the water hit the drain. you'd need to catch the water in a bucket or lay some plastic in the tub to eliminate the tub drain as the issue. Also, you'd need to get the water from some fixture other than the tub so as to eliminate the tub valve as the source.