This is going way off topic, but I can think of many emergencies where I would keep the autopilot in and manage the situation first, rather than trying to fly the machine and deal with the problem identification and then solution at the same time.
Dealing with emergencies is about using all resources at your disposal and there are many that would include using the AP. There are some where your first action would be to kick the AP out immediately. Not capturing a level for instance (though I'd hardly call that an emergency!).
Basic autopilots can't handle much, but the sophisticated ones of the last few years are pretty good and really help you out when the workload gets high.
Not as much as having someone else sitting next to you though!