I would think you would still have the same issue where the sump would draw too much power that the generator would be charging the battery faster and would still kick into full power mode, however you could probably get away with running the generator in short bursts at full throttle to charge the battery then letting the pump run from battery for a while.

I did see a system once where it used the incoming power to pump the sump. there was an electrically operated valve where if the power failed the water would kick on and it would run a turbine to spin the sump pump. It wasted water but was still cheaper in the long run than a flooded basement.

My house has a sump pump but it hasn't ran yet even though hard rains, its in a newer area where the drainage from the house was designed well.