You certainly will lose charge as the refrig/inverter and other 12V draws will be more than the truck is able to replace.
If you start with a fully charged battery your chances are much better of your truck supplying enough charge to keep from completely draining your battery. Of course this depends on hours of drive time and temp.
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2019 Montana HC 310RE
2010 Wildcat 29RLBS
2014 Ford F-350 Lariat 6.7
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