the running power is not the limit on your inverter question. the in rush current to start the compressor will be.

Unless you have an exceptional battery supply I do not see them keeping the fridge running for any length of time. The truck will not likely charge the battery as fast as it is being drained. Probably not even close!

The best way to verify this would be to run the fridge on the inverter with the battery no engine running measure the volts to start. About 2-3 hours later, if still running measure volts again. You should be starting with 12plus volts. If it's just over 11 volts your out of power. I don't see the charging system keeping up with the demand on a fridge compressor. Granted the fridge will shut off when the temp is met. but that inrush to start the compressor again is a massive demand about 5-6 times an hour depending upon ambient temp.. that would be My guess.

This is one of the reasons folks on solar still use propane for the furnace, hotwater heater, stove-oven, and fridge. Those are massive power sucking devices. If they used the batteries they would be drained way to fast!

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