Yamaha 1000w inverter for maintaining batteries

The inverter generator will work if your onboard converter doesn't exceed the rated load from the generator. The combination of the 120V fridge at start up and the draw of the onboard converter may exceed the rating of your generator. I'd assume you could turn off the inverter, disconnect the fridge from 120V power and, having isolated the converter, power only that for a couple of hours to charge your batteries.