One obvious point would be that a plant that burns coal and makes steam cannot change output very quickly in order to meet demand.  Thus they use coal-burning plants to provide a base load, and use natural gas powered gas-turbines to match supply and demand.

I guess my immediate question is whether coal gassification changes this equation??  If there were a plant that was gassifying coal and then piping it into gas-turbines to generate electricity, would such a plant be able to quickly and easily adjust the output to meet demand (and thereby eliminate the need to use natural gas to generate electricity)?

No, coal gasification doesn't change the equation -- and IGCC (integrated gasification combined cycle plant) would be baseload, because they would be so expensive. (I say would be because there are about 5 commercial scale plants in the world, 2 in the U.S., but they are all demonstration plants subsidized with gov't $).

An IGCC plant needs to run and run and run to pay off the investment, and its more complicated to run, start up, and shut down.