Yes, but there could be some problems. You would have to start a siphon to get the water flowing to the pumps volute (area where the pumps impeller is located) first in order to get it started. But once that was taken care of it would work fine. The only possible problem is that if the power is down, the water would have to remain in the volute of the pump so that it could start up again when power is returned. So as long as the water didnt completely empty out of the skimmer back through the input, the pump would always have water in it's volute and would start up again. If for whatever reason in your set-up all the water did empty back through the pump when the power was down, you could add an ant-siphon valve after the pumps output to prevent all the water from draining back through the pump and leaving the volute dry.
That was a long way to say the the pump would NOT self prime.
BTW, why cant you drill your sump for a bulkhead fitting? Is it glass?