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For a drag racer, running an electric water pump drive off a battery that is not charged from an engine driven altenator will release a few extra HP to the flywheel.

For street use, this is not really a proposition as the coolant flow from this system is constant, so it is likely to be too much at idle, & quite possibly too little at full throttle, particularly when pulling up a long steep hill.
If the coolant flow at low speeds is more than you need, then power is being wasted pushing an excess of coolant around at these lower engine speeds.
In a street car, the power to run the pump is supplied from the altenator, which is in turn, driven by the engine. The higher the electrical load, the higher the mechanical load on the engine. If there was any real advantage to using an electric water pump, then i suspect that the car manufacturers would have done it decades ago.