You should be fine running the fridge overnight after running the genset all day. Once the fridge is powered on (the compressor starting is the single biggest power draw of a residential fridge) it doesn't take that much to keep the fridge running on a per-amp-hour basis.
We dry camp all of the time and overnighting is pretty easy. I don't recommend using other electronics at the same time though (so charging phones, laptops, or watching TVs or recording videos, etc.) as they will draw power as well and potentially run down the batteries. Remember also that the batteries are also powering the 12V side of the house, so lights, furnace, etc. may impact battery usage on top of the AC use. Once you know your power budget, you may want to opt for some solar panels to help keep your batteries topped off during the day without using the genset.
When we purchased our new Hurricane, we had the dealer add two more house batteries for a total of 4. We also added 400W of solar panels to charge during daylight since some places may restrict your ability to run the genset. Plus it is more efficient and uses less fuel.
2016 Thor Hurricane 35C with pups Piper and Annabelle
2013 Ford Fiesta toad
FMCA - F457085
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