Not really. At any applied potentional, the arc has a definite resistance, and that resistance is positive.
One could qualify comments about resistance by observing in each case that the resistance is positive, but since resistance is never negative, that would be redundant.
John Larking said "Most arcs have negative resistance, so the current increases without limit, unless there is series resistance elsewhere in the circuit" which is strange thing for someone to say if they understand the behaviour of components that have a negative resistance slope over part of their operating range. The effect of having a resistance is series is that a higher current reduces the potentioal across the arc. In its negative resistance region, this further increases the current. That is, the increasing current is caused by the presence of the series resistance, rather than being prevented by it.
Maybe John genuinely understood the meaning of negative resistance in this context, but I'm far from convinced, and people do have some strange notions at times.
Sylvia.