In a recent patch, downed state was changed so players are unable to use downed skills until the UI animation finishes. But it has happened to me multiple times that when I pressed a (instant) skill right as I got downed, I used that skill, despite the lockout.
Example: Thief, had been pressing 2 for Cluster Bomb the moment I got downed; I had teleported on top of my target, and when the downed UI appeared, I had cooldown on my downed #2.