Well, No. The electricity bumbles around as it is being passed between molocules. It would be rather clumsy, as the new positive atoms are being pulled to the negative, but they switch position and start jumping back and forth. The reason electrolosis works in many things, such as water, is because the hydrogen atoms are more negative and the oxygen are more positive. The changing of electrons makes some of these atoms slightly change their direction, pulling it apart. Also, atoms such as the noble gases don't conduct much because it has a perfect amount of electrons for the amount of protons.
Isn't electricity like a pipe in a loop filled with water, and a pump on the loop, and so water pushes water in front of it but if the pipe is broken (current broken) the flow stops?