Will an inverter run your battery down overnight?

In some parts of the country they would charge that or more just to get out there.

 

2013 Volvo with 3500 watt inverter. 4.5 ci fridge & micro... I just recently killed my 4 batteries after about a 15 month new set of batteries. I think one major thing that hurt they're further longevity was the one time I took it in for a repair, forgot to unplug the fridge... 2 1/2 days afterward, batteries needed a jump & had drained so low, they were never as powerful afterward. Since then I could go about 24 hours without running the engine, that was it! 24 hours, WITH fridge on, ok, after that, loooowwww, volts, needed to start up engine or doa.
Also, I ALWAYS TURN ON ENGINE WHEN MICRO FOOD & MAKING AM COFFEE!!!
Now, just bought new set of batteries, I'm going to stick to basic rules, turn everything off, if gone over 24 hours! I'm even considering a kill switch fer the batts. As others said, the fridge & transformer alone do not kill the batts, unless beyond 24 hours w/o starting or charging via apu. (my apu is about to be fixed)