You'll need to look up the specs for the specific fireplace you have, but the 1500 watts mentioned matches the manual for mine. That's pretty much pushing the limits on a 2000 watt inverter generator and would leave you very little capacity to run anything else at the same time.
While I often use my electric fireplace for heat when hooked up to shore power, I never use it while boondocking which I do a lot of in the cold shoulder seasons. I might use the fake fire for ambiance without turning the heater portion of the fireplace on, but can't see where I would want to fire up the generator for heat when I can just turn on the furnace. To run the electric heat and charge my batteries, I would need to parallel both of my champion 2000 watt generators as 1 of them wouldn't be up to the task.