I have had awakened empires and federations reach enough strength to fight the crises on their own, or at least contain it. It was on higher difficulties though, so AIs with less resource bonuses might not manage.Turtling up against an end game crisis usually doesn't work. It's a great way to fill up your planets if you accept refugees, but even Awakened Empires can't beat a crisis without your help. Though they can do a LOT to contain it if it spawns near them.But Fallen Empires and most regular NPC states will just get eaten alive facing them. And they all get stronger the more they spread.
However the AI is bad at going for the kill and rarely manage to finish them off.