Does the Electric Turbo Really Work?

An electric turbo doesn't work like that. It's going to consume additional energy from the engine, because you need to burn additional fuel to provide additional electricity from the alternator to charge the battery, to drive the turbo. So: No efficiency benefit from a turbocharger driven in this way.

Are electric turbos better?

Turbos are more efficient than superchargers thanks to lower parasitic losses but they can have lag in spinning up while they wait for exhaust pressure. That's where adding an electric motor comes into the picture.

How much HP does electric turbo add?

The electric turbo augmentation in current F1 cars means instant boost at throttle tip-in and adds 150 to 200 hp to the otherwise 850hp F1 engines.