Considering the power grid gets 98% of its power from generators I would say yes. The real question is will it work on a smaller generator independent of the grid?
This all depends on the size of the generator, the steady load on the generator, the transient loads on the generator, and the Thermostat used.
If you are only steady loading the generator at 50% of the continuous rating and the thermostat is the only transient load and it is less than 5%, as long as the generator is properly tuned and running properly you should be fine. If you get too low on the steady load the generator will become less stable and going too high on steady load makes the generator more sensitive to transient loads.
If you have an analog proportional thermostat it should run fine on the generator with small temperature fluxuations in th 1 or 2 degree range. If you are using an on/off the same should hold true.
Also if you have a 25kw or larger whole house auto start generator everything should also be fine as at that point it has enough rotating mass to fight the effects of refrigerators, AC and heating units, or other major electric appliances as they turn off and on.
I hope this helps a little.
FYI - I am a Large Steam Turbine Generator Specialist as well as a Hydro Generator Specialist.
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