With critical loads like a DC refrigerator, it is best to run straight from a battery. This will allow the refrigerator to run at night and at times of low power to the inverter.
Eliminating the inverter from the system also improves system efficiency by eliminating conversion losses and providing greater reliability in the event the inverter fails. The autonomy of a DC refrigerator is longer than an AC unit primarily due to the additional insulation in the cabinet.
*When measured against AC models of the same size & factoring in energy consumed by Inverter, DC models are still more efficient than a comparable AC model.