No, this is the whole "confusing the wave and the medium" problem. Drift velocity (the technical name for "how fast are electrons moving through this wire") has

No, this is the whole "confusing the wave and the medium" problem. Drift velocity (the technical name for "how fast are electrons moving through this wire") has effectively nothing at all to do with the propagation of electrical properties through a circuit. If electrical properties propagated at the drift velocity, there'd be an appreciable delay when you flipped your light switch.