I assume that you have a residential refrigerator that runs off the 1000W inverter. It is the norm to run the reefer off of batteries when on the road. Your alternator will probably keep the battery up during that trip. On RVs, it is absolutely no problem since the alternator will keep the batteries at 100% when running the inverter. In a TT, the charge current from your TV alternator is a lot less since the run is long and the wire size is probably #10 or smaller. I wouldn't worry about it, you should be fine for 4 hours anyway. After all, if it didn't work that way, why bother with an inverter anyway?
As far as vibration, the reefer gets road vibration no matter what...on or off. It is not a problem.
You should confirm that the TV does charge the battery when the engine is running. Sometimes it seems to never really get totally hooked up!
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2015 335DS
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