[Manuel_D]

Not really in the intuitive sense: https://www.youtube.com/watch?v=iph500cPK28

Someone actually went out and tested this: https://www.youtube.com/watch?v=2Vrhk5OjBP8

The electric field is very tightly constrained around the wire. The amount of energy that reaches the light through the gap is incredibly small, not nearly enough to turn on a real light bulb. The bulk of the energy does indeed have to take the path through the wire. I find that video usually leads people to an even less correct understanding than the marbles-in-a-tube analogy.

The Veritasum video can essentially be summarized, "fun fact: two parallel wires act like an antenna, and an extremely small amount of energy reaches the other end before the rest of the energy takes the long path through the wire.