When on gas I think the 12V is only used to control the valves that turn on/off the gas supply to he fridge. So power drain is insignificant. But 12V still needed for the fridge to work.
Typical Dometic / Thetford fridges use no more than 500g gas per day at about 25degC outside temp. In practice much less. So 4.5kg should be fine.
Even last year in the ridiculous temps, Tue - Mon, we ran our fridge constantly, plus heated the water for showers every day, and used the cooker for boiling kettle each morning, and didn’t use the 6kg bottle we had.