Interesting topic. I wrote an article on this very subject for the next issue of Overland Journal. The prospect of using a fridge with only a single battery is highly subjective, so in order to help define your own decision you should examine as much hard data as you can. Start with the fridge and the environment it will be used in. Find out what kind of amp draw your fridge will use in best and worst-case scenarios. For example, when I tested fridges for the Summer 07 issue, the ARB 45 averaged cycling amp-draws as low as 1.75AH when the interior and contents were already cooled down to between 28-32F, and as much as 2.6AH when outside ambient-temp items were added to the chest and then had to be brought down to the lower temps. This was at about 80F outside ambient temps. So if you are in a hot area, or worse, a hot and humid area, then the fridge will work more. So for a worst-case on the ARB 45, I'd figure about 2.75 to 3 AH on average. For best-case, about 1.75AH. I turn a fridge off at night when I go to bed to conserve power and unless it's very hot overnight, the rise in temperature in the chest isn't enough to bother the contents. So for this example:
2.75AH x 17 hours (in a 24-hr period) = 46.75AH
That's just for the fridge. If you use other accessories, you'll need to add those too.
For most conventional deep-cycle batteries (including AGMs like Optima, Odyssey, Orbital, etc) discharging beyond 50% depth of discharge will shorten the life of the battery. So lets say you have a 55AH battery. If you only allow it to go to a 50% depth of discharge, that would be roughly 12.1V - 12.2V which would would occur (very roughly) at around 28AH of use. In this case, you are exceeding the optimum use of the battery to run the fridge for a 24-hr period. Best case scenario with only 1.75AH average, and you are using about 30AH, still a little over the optimum depth of discharge, but not too bad.
I think we all probably abuse the DOD rule, which is fine if we realize that we're ultimately shortening the life of the battery, sometimes by as much as half. Another thing to keep in mind is that the typical AH ratings that we see on the battery label are at the "20-hour rate" which means the battery will provide that many amp-hours for 20 hours when the battery goes flat (10.2V). So for a 55AH battery at the 20-hour rate, that's an average of 2.75AH continuous use (55 divided by 20 = 2.75). If your loads go higher than that, the internal resistance increases, and the higher the losses become (known as the
Peukert Effect). So bottom line: If you use, let's say 6AH instead of 2.75AH, then you will get less than the 55AH rating for that battery.
Do your best to calculate your loads, see what your battery is rated for, and do the math to see how long you can run your fridge on your starting battery. Keep in mind that typical values for battery ratings are when they are brand new, and under optimal conditions (temperatures, etc). Adjust accordingly and use a healthy dose of fudge-factor.