I'm with Scott on the reason behind a bubbler. I'm not totally following what the OP means by output being in the overflow, but at any rate, I'd think you'd want the bubbler to be in the main tank in an area which sees less flow than other parts. You don't want it blowing into your filter's intake because of the cavitation issues mentioned above. Putting it in an area the filter doesn't directly blow current at would help in the tanks circulation and therefore gas exchange.
I've seen numerous mentions on the board about aquariums not needing airstones, but it's been my undocumented observation over the years that in general, tanks with airstones tend to have healthier looking fish, at least at the retail store level. I've got well over a decade of experience at that level and have seen a lot of shops. I'm a firm believer that every primarily fish tank should have extra circulation. It may be that the stores that take the time to put airstones in each tank also take the time to do a lot of other things right, but when I see stores that have tanks full of inactivie fish that are just basically hovering rather than being fish and exploring their tank, the lack of airstones is something I tend to zoom in on.