Almost everything an autopilot should do should have a button and a switch for humans. The switch prevents the autopilot from doing it, the button makes it happen.
This isn't to disparage autopilots, but to assure control. The human should always be in control of the system, and capable of deciding when things happen.
No, in this case, by far the most likely outcome is the autopilot would have pushed the button at the right time, creating no need for the copilot to override it.
How do you figure? Pilot thinks "I think it's time to push the button." Autopilot doesn't push button. Pilot says "autopilot is broken. I need to override." Pilot pushes button early.
If the pilot thinks the button needs pushing, they're not going to wait til after the crash to see if the autopilot is working.
What happened here wasn't that the copilot sat there waiting for the intended time to come about and pressed the button exactly at that intended time and just didn't know what the time was supposed to be. What happened was that he was frantically trying to concentrate on a zillion things at once and pressed the button a bit early because he thought otherwise he might end up pressing it too late and he had been warned about the dangers of pressing it too late but not about the dangers of pressing it too early. If there had been an autopilot, most likely the autopilot would have pressed the button at the right time while he was looking at something else.
