No, you're correct. The changing B-field from the spark action creates a changing E-field as part of a small EM wave that propagates out from the spark itself. A spark gap is generally not a very effective radiator, because the gap is small (1mm or so) and the time constant is on the order of a nanosecond or so. With really high voltage like from a TV picture tube, you could probably fire a 35kV arc with a length closer to a few cm where the GHz bandwidth of the arc might make it a more efficient radiator.
I don't have any great info handy on how to calculate the ionization process that leads to the spark (I used to). Here is the hit list from a quick google search in case it helps.