Group 27 deep cycle battery + 2000W inverter

No one will be able to give you a true answer, not enough information and too many variables.

Group27 battery is pretty light on capacity, that is an obvious fact.

Group 27 can supply enough energy to power your furnace overnight in cool temperatures, but it will be pretty deeply discharged by morning.

Your inverter unless it has a "power save feature" is going to eat up 1 Ahr-2Ahr of battery capacity per hr just doing nothing. That is 24Ahr-48Ahr per 24 hr period.

Home fridges vary widely with how much energy they will use, some pretty light like 90W (.75A at 120V) to upwards of 780W (6.5A at 120V) and may run perhaps 20-30 minutes per hr..

So, no one is going to be able to answer your question.

My suggestion is try a dry run in your driveway or backyard (where ever you park it) and see just how long you can run the fridge..

My bet is you will need more capacity than a group27 if you want it to run more than 12hrs..

Probably for an overnight stop you will be fine. Assuming the fridge is already full of cold food. Even then if it shuts off you should be good for another 6 hours if you keep the doors closed. Also assumes no use of the furnace and minimum lights.

As other will tell you a Group 27 battery is not a "true" deep discharge battery. The only true deep discharge lead acid batteries are 6V golf cart batteries, size GC2. (One marine/RC Group 27 battery has about 80 amp-hours of power @ 12V; 2 golf cart batteries have about 215 amp-hours of power @ 12V.)

There are too many variables to answer your question. Size of the refrigerator and the amount of power it draws is the first one. Ambient temperature is number two.

Assuming that the refrigerator starts fully cooled with fully cooled contents and YOU DO NOT OPEN THE DOOR, maybe 12 hours.

A group 27 with how many amp hours fully charged? A 12 volt or120 volt fridge? A full size fridge that uses how many amps when running? If a 120 volt fridge, how efficient is the inverter?