I've been to Disney World over 60 times with trips ranging from one day to 18 days. In all that time, I've been stuck on Haunted Mansion once (for about fifteen minutes) and its a small world for twenty-four hours. OK, it wasn't 24 hours, more like ten minutes but it seemed longer with that song constantly playing!
Will a ride stop momentarily? Yes, that's common, especially on the continual loading rides if someone if having difficulty getting into the ride vehicle.
I really wouldn't worry about it too much. The chances of you having to get evacuated from an attraction are really slim.