Most Important: You waste the Battery if you cycle it with no use.
And now your question:
Your powersupply might be a little more effective, while charging the battery at the same time while you run the computer. But the effectivity of the batteries while eat that. The Batteries need much more energy to charge, as they give back while they discharge.
So in general it ist a really bad idea to unplug your computer to save energy. It will not work.