An advanced autopilot is a major bonus during an emergency as it reduces the workload of simply keeping the aircraft flying safely, enabling more attention to be devoted to dealing with the problem. These days airspace is more complicated and congested. Tolerences are more critical and setting up an approach much more involved.
Depends entirely what sort of emergency or just merely the garden variety "Non-Normal" like a generator, pack, uncommanded pressurisation and so on.
The discussion is more about an undue attraction to automatics like the example I observed when a crew took up an instrument approach holding pattern using the magenta line and heading bug to trace their flight path over the magenta line holding pattern.
Pity that a minor programming error placed the holding fix which was a VOR, some 15 miles from the actual VOR and that over the fix the VOR/DME showed 15 DME which you would have thought would have picked up by the crew as somewhat unusual. At the same time the VOR/RMI needle was pointing to where the actual VOR was 15 miles away.
Fortunately it was in the simulator since the real aircraft would have eventually flown into a nearby mountain caused by the crew blindly following a false position magenta line. The reluctance of some crews to cross check frequently with basic navaids during even a normal flight is symptomatic of the inherent dangers of automation complacency. It is plain laziness.
When in the simulator, you see an experienced pilot furiously programming a visual circuit into the FMC, when in the first place all he was asked for, was a take off climb to 1500 ft, turn downwind at 30 degrees angle of bank, maintaining 2 mile spacing from the runway clearly visible from his seat using raw data and manual flying with no autothrottle, turn base and land - all in CAVOK - then you have now seen the archetypal automatics dependant pilot.