I certainly haven’t looked into this or run the numbers or anything, but at first blush I think there could be some efficiency gains here. It’s my understanding that generators tend to be pretty inefficient at low loads. Normal (non inverter generators) have to run at a specific RPM in order to maintain the proper frequency, so even if you have a very low load (such as you would at night) the generator will still run at a high RPM and use a lot of gas.
If you could run the generator, say, for 4 hours at a high load to charge the powerwall, then use the powerwall overnight I suspect that even with the 10% round trip loss in the powerwall you would wind up saving a considerable amount of fuel versus running the generator for 12 hours to support a very low overnight load.
This is the same principal that (non plugin) hybrid cars work on. Other than getting a minimal amount of charging from regenerative brakes, the only way they can charge is by using the gas engine to drive a generator and there are losses in the generator and in the batteries. But by optimizing exactly when and how much the car charges the batteries it can make sure that gas engine is operating as efficiently as possible and is in that way able to save more energy than is lost in the conversion to electric power.