It's a good thought, but there are some errors in your idea. The generators use fuel according to the load, similar to a car, which is why always specify runtimes at a specific load. More load, more gas being used. The newer generators (I'm thinking specifically of the Honda EU series with the eco-throttle), automatically adjust the engine according to the output. In that way, they are able to save gas if the electrical load drops off.

Also, recharging a battery is not 100% efficient, so you will lose some energy there. I think it really depends on the conditions you use the generator for, it might be useful under certain conditions. Actually, you might want to search on something like that, I think it might already exist.

just did a quick search, i think this is similar to what you were looking for

http://www.cumminsonan.com/rv/products/ec/