The voltage is much higher than that...at least 20 kV and probably more like 30 - 40 kV. I think you are right that in your first test, the potential was just shorting out across the plates of the capacitor. The capacitor had less resistance than the plug. It may have even welded a few of the plates together, creating a dead short.
Capacitors pass ac, but store dc. But the diode wouldn't allow any ac to pass. So (if the capacitor could handle the voltage), and assuming we are starting with a discharged capacitor, the capacitor would charge and cause a resultant drop in the voltage during the charge. As the voltage rises to a level allowing it to jump the gap, some (but probably not all) of the energy available will be discharged across the gap.
It seems possible that with this system, changing the spark gap could actually alter the timing. It would be quite convenient to use this method to adjust timing quickly on a bike; what is the availability and cost of capacitors that will handle this voltage?
I think the high voltage discharge produced by the coil is at least mostly dc. It's a build up and release of energy. CDI stands for Capacitor (or Capacitive?)Discharge Ignition.
If ac was coming out of the coil, you would only make use of half of it with only one diode, because you are only rectifying half of the waveform to dc.
The fact that your diode works better one direction than the other is probably due to the polarity of the components working together. I wouldn't be surprised if the diode is already fried and there is a spark jumping a gap inside the diode. Got a Fluke?
Where I get really foggy on this is what the spark devices are trying to accomplish? Longer duration? Is there more power to be gained this way?