YES.......normal
Flame (or electric element) operation is controlled by thermostat. Heat is used to turn ammonia in vapor -----ammonia vapor gets condensed back into liquid-----ammonia liquid gets 'flashed' back into vapor when it mixes with the hydrogen gas.....that ammonia vapor absorbs heat from freezer/food sections cooling them down. The ammonia vapor turns back into a liquid and collects at bottom of fridge.
Heat (flame or electric) is then needed to repeat the cycle.
So flame/element turn on/off as required based on thermistor sensing of temps in food section. Thermistor sensing is then used by thermostat to control propane or electric element function.
Same concept with your RV Oven, Water Heater and Furnace----thermostat controls when/how long flame operates.
Actually.....include the A/C Unit. Thermostat controls it's cooling function just no propane used.
Caveat:
OLDER absorption fridges prior to electronic controls etc.
Flame was ON all the time.........manual setting of thermostat 'position' (MIN to MAX) controlled size of flame. More cooling need ---turn up thermostat and flame got bigger. Less cooling needed----turn down thermostat and flame got smaller.