This is a camper
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While this is a trailer
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Unless the converter manufacturer clearly states its product can serve as a standalone power supply I would call the manufacturer about this.
And if your travel time to and from to the campground is always less than 2 hours each way my vote is to buy a car battery, not an RV battery. You will save money and get a 5-year minimum warranty. Just do not fudge about running around with more than a tiny battery load to and from the campground.
Batteries act as shock absorbers for cheap converter dirty power which is called "ripple"