From a technical standpoint it could be done as you describe. This issue is really how practical would it be. Need some numbers to see how practical.
1. How much current is needed to start and run the refrigerator.
2. How long at a time do you anticipate to run the refrigerator without shorepower.
3. How many amp hours is your battery?
Even with good numbers I would install switches to control how the refrigerator is powered. Only use the inverter when no shorepower is available. Actually a relay arrangement could be done to do this switchover automatically.
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Chuck - Sparta, TN
2012 Jay Flight 22FB, 2 x Honda EU2000i
2013 GMC Yukon XL Denali AWD
EDUCATION is what you get when you read the fine print.....
EXPERIENCE is what you get when you don't.
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