A small 6.9 cubic foot absorption fridge draws 5.7 kwh in a 24 hour period with a duty cycle of 2/3. i.e. for every hour the fridge will run 40 minutes.
The wattage draw while running is about 325 watts. Allowing for inverter losses that works out to about 32 amps of load on the alternator.
Alternators may have about a 1/3 duty cycle so a 120 amp alternator would prefer to have a load of only 40 amps continuous. Modern vehicles draw lots of amps, so powering an inverter to run the fridge may exceed the continuous duty cycle of the alternator.