Rik, I see no reason why not. I have a 3 way fridge and the gas burner has two settings high and low. Even on high the flame is very low and would use very little fuel.
Mind cant get my head around that you boil a liquid to produce a cold fridge!
Dave
Rather than thinking of heating the liquid think in term sof increasing its pressure by heating - then when you let the liquid escape (lose pressure) it cools just like gas out of a cannister.