No.

Imagine sledding down hillside covered in gravel. Friction imparts momentum from your sled to the gravel, causing a few pieces to slide forward with each ride down the hill. With a thin enough layer of gravel, and with enough ride down the hill, you can end up with bare patches with no gravel.

In this loose analogy, the gravel is atoms in wire. The sled is an electrical impulse. Maybe there's some tunneling that takes place when the gravel moves from one site to another, but I'm not sure.

(I once had a job offer from Intel to work on electromigration in next gen chips, but didn't take it, so I don't know much beyond the basics.)