while it's a not a 'bad' idea, if the fridge is not already powered by the onboard inverter, it would not be a simple task to just 'add an inverter' for it, since it has to have power from not only the propane, but also the ATS(auto transfer switch) when you are plugged in or are running the generator.
That would require wiring the inverter output to the Main breaker panel, and the inverter would have to have an internal relay so that it does not interfere when Shore Power or Generator power is available.
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