600w should be plenty for normal running, but sometimes the peak load is much higher. The ice maker uses a heater during the cube eject cycle and that adds more amps. Some fridges have a high humidity gadget to remove condensation too. A peak will occur if one or both of these cycles on. Check the fridge rating for the rated amp load for the supply circuit - that will be the peak.
As others have said, the inverter usually has a higher peak load value that it can handle for 2-5 minutes. Check to make sure you know both the sustained and the peak output of that inverter. Some manufacturers like to advertise the peak value to make it look better.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL