I'm not sure about destroying doors in general, actually. But something to try at least.
does the AI have a 'path' through such open doors?
The AI definitely acts depending on the open/closed status. Destroyed or not present should count as open.
Once in mansion, when it still had the doors, a unit of mine opened a door. Then there was an alien right behind the door. I had no movement left and couldn't dispose of or disable this alien in any other way, I only had enough movement left to close the door again. It didn't attack on its turn though it could easily have killed me, which it certainly would have done, if only it had opened the door. (They do open/close doors sometimes, even those that should not be able to like hovernets - they don't have hands!)