I had a Mini fridge rated at .8a at 120Vac for a bit, ran it on the system for a while and gave it to the MIL because the freezer was too small. I wouldn't even think of trying it on the Grp 27, that's a good way to kill a battery very quickly. Even quicker for our five year old battery.
New and fully charged our grp 27 with 95 Ah was pressed to run just our 12v absorption fridge pulling 8 amp overnight. It never cycles but also has no start up surge or needs a inverter. The cycling would help but the start up surge will be harder and harder to handle as the battery loses voltage.
That surge takes a chunk out your battery's power every time. Eventually the battery will be low enough that the compressor doesn't start and the continued attempt will drain the battery the rest of the way. I've watched it happen testing the little A/C on a 250 Ah 8-D. It damaged it and the 3000w inverter, surges are nothing to ignore. Starting and marine batteries can't take that kind of abuse and it will shorten the life of even GC batts.
8 amps or .8a at 120Vac is on the low end for mini fridges. The majority pull 1.5a at 120Vac and have even higher start up surges to deal with. Only one pulls less than .8a and it cost a extra $100 for that .16a savings. That's a extra 1.6a not coming out of your battery. ( mini cubes are almost always 1.5a @ 120Vac)
Just adding info to hopefully help you set it up.