Install the inverter and don't look back.
No one has mentioned they actually installed an inverter to power the fridge and regretted it.
I have run my absorption fridge with my 300 watt Go Power inverter and it worked fine. Typically I run on propane but the igniter did not work that day and I needed to get on the road. My inverter got me going and kept me going until I could get the propane to light eight hours later. Just saying worst case you have a backup system.
May also be convenient to charge small items on the road without running the generator.
Go for it.