What is the relationship between Power Generated in the grid and Voltage delivered?
For one thing, turbine plants use much higher voltages than 120. 4140V or 12kV are more typical for a large turbine, with that voltage stepped up further for long lines distribution.
For another, a turbine like you describe would be only for a backup generator. Large turbines for a municipal-size grid use steam heated by the fuel, be it natural gas, coal or nuclear fission.
Anyway, what happens with any generator linked to the grid is that they vary the torque to match the load, while keeping RPM constant. This is because the generator's waveforms not only need to be the same frequency, but the same phase.
For example, windmills in groups run at the same RPM together, varying their power output by feathering the props and thus varying their torque, but all in lockstep with the grid frequency and phase.
Think of it like what happens when your car climbs a hill at a constant speed: the engine RPM doesn't change, but to maintain speed you have to give it more accelerator to increase the torque, and thus, the power (power being basically torque x RPM.)