This would apply for a sustained gap, where no re-contact between conductors would happen to re-draw the arc. And in reality, we can see these series arcs happen with very very narrow (smaller than a millimeter) gap. In addition to the air gap breakdown voltage, there is a voltage drop characteristic, much like seen in semiconductors, whenever you have transitions between different metals and the arc. I have only found a small amount of science on these aspects of arcs. But they do play some role in gas-discharge lighting.
