No, since the power electronics and on-board charger on the car are designed to handle sudden power cut.

What in practice happens is:

• EV notices the power pins are not energizes, the actual charging electronics and battery is designed to handle this. Various protective snubber circuits built in the power electronics eat any voltage shift spikes that happen as result. Charger in controlled fashion goes de-energized. As said it is designed to handle this.
• Upon the wall Electric Vehicle Supply Equipment ("11kW charger") losing power, its biased to open contactor springs open. The EVSE must provide constant pilot signal to its contactor (big fancy relay switch) to keep it closed and thus power pins energized.
• Also the power to the pilot signal sent from the EVSE to the car is cut, since the control circuit goes powerless. This will cause the EV to cut its own pilot to its internal contactor, isolating the connection double. Since no pilot from the wallside is one of the safety conditions of "Something abnormally, cut connection"

So charger will just suddenly lose power, but that is not a problem. Both the wall supply equipment and the vehicle electronics is designed to handle such circuit trip condition.

The system is designed for robust use out in the world in harsh bad conditions. It isnt ones cheap consumer electronics, where exactly something like sudden power cut might scramble things. For example the car doesn't even lose power. All the EV control circuitry runs on the internal 12V battery, not of the wall feed or even the main traction battery.

What mostly happens is you probably hearing sudden cascade of clack-clack-clack as the various isolation contactors all spring open in simultanous quick succession upon the power and pilot signals diappearing. Not to worry, that is exactly what is designed and supposed to happen upon power trip. The design doesn't want contactors keeping connection existing in case power comes back on suddenly. So on power loss contactors open to isolate the vehicle from power. Only to be closed again in controlled fashion on the order of the control circuits, should power return.

The charger itself is basically just a fancy power switch.

Cutting power to It won't harm the car.

For what it's worth, I cut the power when charging my ev everytime because I want to charge only between 22h00 and 6h00 (when power is cheaper). I've done that for more than 2 years now and never had any problem nor did I see a downgrade in the autonomy of the battery (peugeot e-208).