I have this skimmer.
1. The overflow gravity is used to push the water through the whole system. If you can't set it up using the T or Y pipe, then you would need a small pump to feed the water.
2. You still need another pump (i.e. oceanrunner 2700) in order to run the venturi wheel and create micro bubble.
So you are looking at at least 1 pump, possibly 2.
Mine's setup so that the overflow water is split through T pipe. One end goes directly to the filter in the sump and the other goes to the skimmer. I have tried every possible scenario with this thing, trying to get the best efficiency out of it. When I tried to run it without any pump and purely the overflow pressure (JUST LIKE how you initially suggested), the water moves, but you don't get the micro bubbles. When I tried to run only the oceanrunner 2700 without the overflow, there was a lot of bubbles, but not enough pressure to circulate the water. Basically the water was sitting in the chamber and not exiting. The best setup is what the manufacturer suggests. Get the oceanrunner 2700 (or something equivalent) and also use the overflow pressure.
FYI, if you look at the picture in the previous reply, do you see the little grey pipe in the mid section that is somewhat leaned to the side? That's where you feed the overflow water into. And then the exit pipe below that toward the bottom of the skimmer is where water would be inputed into the oceanrunner.
Hope this helps!