it depends largely on ambient temps
we had our ARB running in La Jolla, CA for several days with no problems. Two days in Baja (Todos Santos) ran the spare battery down to nearly nothing. And we even ran the truck for 15 minutes in the morning and evening to help top off the batteries.
"Running the truck to top off the battery" doesn't work. At idle it takes hours to get any significant charge into your battery. Look at it like this: if you have a 60A alt, at idle you might produce 10-20 amps beyond the needs of the engine (computer, ignition coil, relays, lights, stereo, etc). If you apply 10A to a battery for an hour, you don't get 10amp hours of battery time, due to internal resistance and other inefficiencies. You get less. So if you have an 80 amp hour battery that is at 50% charge, you are looking at more than 4 hours of running to top off the battery. Driving will charge the battery a little faster (higher rpm=more juice) but it still takes time.
One thing that does work better--- if you do turn the truck on for any reason (re-parking to get the fridge out of the sun, for example) then do let it idle for an extra couple of minutes, but be sure to crank the fridge to "coldest" while you are doing that. That way you are storing energy as cold as well as storing energy in the battery. Just be sure to turn the fridge back to a warmer setting when you are done.
All in all-- you'll probably find that a spare battery is a good investment if you plan to live out of the fridge for any length of time. A solar panel, while $$, is also a very good investment to keep the battery(ies) charged up. Even if the panel(s) can't supply enough to run the fridge, they will extend the life of the battery that you are using.