Centrifugal vane pumps (basically what all the pumps used in aquariums are) are not self-priming, but your illustration would probably work if you primed the pump manually. Fill the skimmer by hand, while plugging the pump input and skimmer output. Then un-stop the pump inlet, and plug in the pump. The water in the skimmer body will flow back out through the pump, filling it with water, at which point the pump will be able to start pumping, and this will work until you unplug the skimmer (to clean the cup) or until the power is interupted. If the pump lost power, it would not reprime. And it could overheat.
You can prevent that potential problem by adding an S-trap on the right side of your drawing. The pump inlet pipe would come out of the water, go straight up until it's an inch or two above the pump inlet, then it would turn 180 degrees, form a U down towards the water, and come back up to enter the pump inlet.
It will look like an S lying on it's left side.
This should hold water in it when the pump is unplugged, so it can reprime by itself when plugged in again. You'll probably want to do something like this so you don't have to reprime it manually every time you need to clean the skimmer cup.
Nate