Maximum current in a power supply
It depends on how fridge and power supply react to overcurrent (power supply) or voltage drop (fridge).
The high peak current is due to the start-up current of the motor in the compressor. It will start fine with a lower current, it will just take a little bit longer. So as long as the fridge does not have any monitoring that switches the compressor off at input voltage drops you will be fine (from the fridges perspective).
The power supply has to handle this as well. If the output voltage just drops until it can deliver enough current, then this will work. If the output of the power supply switches off immediately in case of over current, then you will have a supply that constantly turns on and switches off again.
As you can see there are a lot of ifs in this answer. This is because we neither know how your fridge reacts, nor what your power supply will do. If you are sufficiantly sure that the power supply has some kind of protection (so it won't blow up) you can just test it. The fridge will take no harm.