IANAEE (not an electrical engineer), but doesn't a gas turbine spin at a constant speed to drive a 60Hz generator, regardless of whether it's running at 20%, 60%, or 100% of capacity?
For an on-line gas turbine, the time to ramp up production is the second or few needed for the automated controls to open the throttle on the "Gas IN" pipe. It's basically a natural gas-burning turboprop jet engine, with the propeller replaced by a generator. (Yes, this can be less efficient in a combined cycle plant.)