I would agree that there is no problem with dry camping and a properly installed residential fridge. However, going into it one has to realize that properly installed should include a robust solar system and proper sized battery bank. 4 or more batteries should do the job. The more the better. If you will only be occasionally dry camping a couple of 160 watt solar panels will look after the needs of the fridge. However if frequent and long term dry camping is planned I would plan on around 400 to 600 watts of solar. This will allow for some bad weather before having to start the generator. However for people like us who are power hogs and use microwave, toaster, coffee maker, magic bullet juicer, 36 inch TV, computer etc etc etc a generator a couple of hours per day is going to happen anyway. For us usually an hour at breakfast and an hour at supper. Its just how we role. If we didn't use all that stuff then the solar system would have no problem keeping up with the fridge by itself.
Oh and on edit, you should have a robust charging system so when the genny is running it puts a fast charge on the batteries. 80 to 120 amp 3 stage charger etc etc.
Good luck with the change over. You'll never regret it...if you do it right. :)
