On the aircraft I’m most familiar with (primarily business-jets), it’s a regulatory requirement that the pilot be able to physically overpower the autopilot and its associated actuators in the case it runs away and tries to go hard-to-the-stops in any particular direction.
The flight test to demonstrate this capability involves:
1. Warn the pilots (who are expecting it; it’s a planned test flight) ... Three ... Two ... One ... Now!
2. Pilots wait two seconds to simulate how long it would take to recognize the hardover were it was unanticipated.
3. Pilots override controls to recover.
The problem the AF447 guys may have run into is that they had a hardover, but due to the turbulence didn’t recognize it until they were significantly diverted from straight-and-level. If at the same time they lost instruments, they wouldn’t have known what to do to recover even if they did recognize it.
That would suck. Big time.