Yes. If your airspeed is unreliable, AP engagement won't work. (Anyone, please correct me if I said that incorrectly).
When the plane reverted to Alternate Law (2B if I remember correctly), engaging the autopilot was not an option. Once latched into alternate law, the autopilot can not be reengaged until the system is reset on the ground.
My only questions still outstanding in this mystery (outside "What were they thinking") is why with several nose-down inputs to the control stick, some lasting several seconds, why the elevators never moved into a nose-down position. With old cable controls, if you put the stick all the way forward the elevators would instantly respond with nose-down movements however, in the Airbus fly by wire, the elevators never got into a nose-down configuration despite several full nose-down stick inputs. They began to move a bit but were still in a nose-up position the entire ride down. I've wondered if there is a cumulative effect with all the nose-up inputs that delayed the movement of the elevators. The THS I understand...since the elevators never moved to a nose-down position I wouldn't expect the THS to move that way either. I've asked that question a couple of times and no one seems to know
Edited to add: Looking back at the traces, there is around 15 seconds of nose-down stick from 2:13:45 to 2:14. The elevator was at 30 nose-up and in that 15 seconds of almost full nose-down stick, the elevator only moved to 15 nose-up. So even though the pilot commands nose-down, the fly-by-wire never moved the elevators to a nose-down position...for 15 seconds!!! As they only had a bit over 4 minutes from start to finish, I find that response time to pilot inputs awfully slow. Granted, by this point, it was to late to recover but if they had begun a recovery much sooner, such slow response to pilot stick input would have made recovery very difficult, especially considering the THS never moved from full nose-up. If it only moves 1 degree per second, that would mean almost a full minute of full nose-down stick would have been required to get the elevators to full nose-down with the THS beginning to move that way at some point in the process. So just how long would it have taken, with full nose-down stick, to get the elevators and THS into a nose-down position??