Does ion weapon damage stack with cloaking and teleporter cooldowns?

The teleporter and cloaking device use a similar "cooldown" period to the ion weapons lockdown. Do those two abilities stack?

In particular, if a ship cloaks, can I ion the cloaking device during the cooldown period to prevent him from cloaking again?

Yes, assuming the ion device does sufficient ion damage, you could lock it down while it was on cooldown. Note that if you only do partial ion damage you'll reduce the effective level of the cloak. Though that is typically more than enough; a cloak has a pretty long cooldown by weapon standards. You can keep shooting him too, and it will keep adding ion damage. I've never seen ion damage pile up I should note; I said it "reset the timer" but it's possible I was just seeing ion damage when the previous "debuff" had run out.

How ion weapons work. To answer your question in the comments, assume the enemy has a level 3 cloak, and you have a 1 point ion weapon. Hitting the cloak with your 1pt ion weapon would do a one point of ion damage, which is worth 5 seconds"disruption" and 1 power bar of damage. This will "disrupt" the cloak and reducing the cloak time by 5 seconds (the "answer" below is correct on that).