[vteco]

Yes, you can easily use electricity (through electrolysis) to separate water into oxygen and hydrogen.

Yes, you can burn them together to release energy in an engine.

No, the amount of chemical energy you store from real world electrolysis, and then feed into internal combustion won't equal the amount of electrical energy you had to put in to start with.

You might as well just feed the electricity into an electric motor, and avoid the inevitable losses you get when jumping through hoops from one energy type to another for no apparent reason.