ARB and likely others will draw and then cut-off at a set voltage. I kept mine plugged in while running, but would shut it off when I wasn't running if it was during say a road trip and at night assuming it's still fairly cool, it's just like a cooler. I would set the temp near freezing and then if it warms up to around 36F or something that's considered safe anyway, then no worries.
I have some slightly more extended stays and I'm out when it's very warm, so I went AUX battery and added the ability to maintain the battery using solar.
Quick rant, the Generators you see called Yeti, Jackery, stuff like that, beware of because often they require like 11 hrs to recharge using solar and 6 or 7 hrs at an outlet which are all unrealistic besides one time use, That's almost useless unless you size it massively more than your needs, which doesn't make much sense. Just get a marine or deep cycle battery and build your own setup as you can afford it or until these units become more realistic. One day those generators will be awesome, but not today imo. I have no experience with them, just wanted to buy them until I saw how long they take to recharge vs their capacity vs an AGM battery, which I still think is a bit high dollar. I think you may have more use from one of the Li battery jumpers.