Ajb,
Normally the problem is the opposite.. the Op wants to know if the main drain is working, so they shut off the skimmer and any other input to the pump, and then they open the main drain.
If the main drain is connected then the pump should get plenty of water and will continue to run... BUT... If the main drain has been plugged or is not open, the pump will very quickly run out of water. All the water in the pump basket is pumped out, and no new water is coming into the pump. This is ok for a very short period of time, but running without water is never a good idea, and can lead to pump damage.
Closing the main drain will often help the skimmers work better as you get a little more water flowing through them.
The real key to good skimming is a weir door. The weir door floats up and down between the skimmer's mouth and the Skimmer basket. If you don't have a weir door it means your skimming will be reduced about 50% or more. Many people think the weir door just prevents the stuff floating above the skimmer basket from come backing out into the pool. That is true, but the main job of a weir door is to 'skim' the surface water into the skimmer.. This why they call it a skimmer. It wants to capture all the stuff that is floating on the surface of the water.
Thanks,
Jim R.