The HWS doesn't have a pilot light, it will restart when the temp drops, gas valve opens and igniter sparks, no pilot lights on fridge or HWS............I think they burn at 10j/hr so you would burn a heap of gas for nothing just keeping the water hot, most just put it on 15 mins before needed.........................................if you connected to the thermocouple you would be opening up a can of worms, having played around with a couple they are very touchy and a slight push out of position, dirt or spider web and it will shut the gas solenoid.....................I think the biggest problem is having the alarm operate in set parameters or the thing will go off when your cooling your fridge, a simple switch would do it so long as remember to turn the thing on once at op temp.................................If worried about running out of gas then some nong pulling your power cord out at a park should also be in the equation, actually happens more than the gas I think, so a system that alarms when fridge temp climbs would be better and cover all bases.
A look at Jaycar could possibly save a lot of brain work as I seem to recall a simple circuit kit which would do the job, works on a temp sensor with little buzzer.............
It's a good brain exercise working out way's to do it that don't get overly complicated.
The tag on your fridge will tell you how much gas it burns in joulles per hour, a 9kg bottle has 4000j I think so if free camping with the fridge on gas and since it burns the whole time at a fixed rate simple division will tell you how long things will last, thermostat on fridge regulates the refrigerant flow not the gas flame.........