Now that I'm more awake, I see I made some errors in my previous post. Looking at the Honda generator specs, you are NOT 2x more efficient at 1/4 load, you just get roughly 2x more runtime. If you calculate it out, you are actually about 2x more efficient in terms of energy/gallon running it at full load.

So what this means is that the advantage to a battery/inverter setup changes. You will probably not see much of an advantage under small, constant loads (like a continuous 50W lightbulb). Either way you are using a set amount of energy, either straight from the generator or from the battery bank. Using the generator, you are operating at a less efficient part of the power curve, so you waste gas there. However, using a battery bank will allow you to run the generator at peak efficiency (full load), but any gains in efficiency will probably be offset by the ineffeciency of the battery/inverter setup. Of course this all depends on the charging efficiency and inverter efficiency, I'm using an estimate of about a 60% efficiency for those types of systems. Under those conditions, I don't think you'll see much of a gain.

Where your idea will really shine is during intermittant loads. If you're running a few lightbulbs continously, and need to power a pump, refrigerator, A/C, only occasionally, then you will see an advantage. If we assume your peak load is about 5kw, instead of needing to run a large 5kW generator continously to power only 100W most of the time, you can run a smaller 500W generator to power the small loads and use the batter/inverter as a buffer to handle the peak loads. Then you will see the efficiency gains from running a smaller enginer rather than a larger one. Again, this all depends on your continous and peak loads.

These are all assumptions and rough calculations, so I wouldn't put a whole lot of faith into it. I'm just rambling off the top of my head.