To be totally blunt, you are totally wrong. But you are in good company.
The resistance of the earth is not exactly zero. But it is so low that for all practical purposes it is zero.
Individual electrons do make the whole trip. They just move a little more in that direction, as do gazillions of other electrons along the way. There is a very very small but finite voltage gradient that moves the all. The actual voltage gradient within the earth is a linear sum of all of the voltage gradients from all of the circuits that are completed through the earth.
But there are far higher voltages and currents within the core which are responsible for the Earth's magnetic field.
Finally, if there really is no earth path to the source the elections will not just wander around looking.