To directly answer your question is that any refrigerator that has a single speed AC motor not routed through an inverter will not run well. The reason for this is related to how AC brushless motors work. The AC power interacts with the windings and magnets to turn the motor at a specific RPM. With square wave, including modified sine wave inverters the distorted wave form tries to stop or reverse the motor in mid cycle. This produces heat vibration and unnatural torque forces. All of these are hard on the motor and reduce its efficiency. All filters do is add capacitance to the circuit and potentially shunt wildly out of frequency harmonics. This is effective at reducing the noise in lower quality radio equipment. It won’t help a refrigerator. You can get refrigerators that are certified for MSW (square wave) inverters. Typically they have DC rectifiers and a downstream inverter for precise motor control. Again the speed is dependent on the frequency of the AC power (load dependent). Samsung is a common make that does this.
