heat pumps just run something similar to a reverse Carnot cycle on their refrigerants and use a condenser coil to release the extra heat to the water. So for all practical purposes it heats the water inside the tank in a pretty similar fashion to how a normal electric water heater works, it just delivers it from a slightly different source and it isn't electric resistive.

So no, not possible. Theoretically you might be able to do it with a stupid enough system of coils and a very ridiculous amount of power, but it wouldn't be efficient or practical.