Whilst it's true that higher voltages generally means lower currents and vice versa, in supply terms, it isn't true when the resistance/impedance is a constant. It may be that at a lower voltage the motors may struggle and overheat with the same, or lower current and cause the overheat cut-out to operate.I disconnect fridges and freezers during a low voltage period. I believe the lower voltage means higher current which can damage the mtor/pumps.
However, disconnecting appliances during any supply fluctuations, especially caused by lightning, is a wise move.