Problem isn't the alternator keeping up, it is the factory wiring usually will not carry 100% of the frig 12v load.
When checking battery level by voltage, you need to disconnect all loads, wait a few minutes for the battery to equalize, then measure the voltage. When the load is still applied, the voltage will be much lower than true voltage.
However, a group 24 is only rated at 90A/hr. 14A for two hours is 28A/hr or about 31% of battery capacity. If the fridge was still on when voltage was measured, 11.77 would seem about right.