Generators run most efficently loaded 75 to 90 percent of rated capacity. When you are running at low loads the losses from just running it wastes fuel.

I don't know if anyone makes a specific unit that combines a battery bank but it has been recommended for a long time to combine the two. That way you can properly load the generator by charging the batteries while running light loads.

While batteries and inverters aren't 100% efficent you gain in the long run.

The best way to use such a setup is to only run the genny when you are want to run heavy loads. Short term runs rather than continuious runs. I.E.The refrigerator, water pump, furnace and the like. Also to charge up the batteries. Then you shut off the genny. Then you draw continuous light loads from the battery bank. Things like the lighting system or radio.

Such a duel system can greatly stretch your fuel supply since your heavy load period are relitively short duration. And to operate best you need to schedule operations to sequentially perform them in a block.