Hi,
not really done such stress test yet, but I would definitly avoid 1000 fsm on mobile devices... on desktop and web, I would suspect no real issues leaving all fsm enabled. One thing to avoid in your set up is to have the 1000 fsm running something int he game loop, that is all doing something, if they simply wait for an occasional event to occur and react, then fine.
A state with nothing in it will not impact on perfs, at least that's what I experiencing so far. What would impact is a gloal event called during the gameloop. If you have 10 20 100 of them, fine, 1000 would definitly start to be noticeable.
Physics is likely the area where proper set up would make a huge difference in terms of perfs. for example DO NOT implement a TriggerStay or CollisionStay global events in these 1000's fsm.
What are your 1000 fsm anyway? ennemies?
bye,
Jean