At any point after the initial upset and once the initial period of pitot-iced UAS ended, did the systems on board AF447 have sufficient information about the aircraft's attitude/altitude/speed(s) to ascertain and deliver the appropriate recovery inputs? (i.e. would the kind of Hail Mary recovery systems on Cirrus and some other aircraft have worked if the big red button was pushed?)
The answer to your first question is an unqualified YES!!! They had attitude, altitude, and vertical speed information. The nose-high attitude was THE primary clue that they were indeed stalled, and the unwinding altitude and vertical speed verified it. If they had only recognized those basic clues, they could have recovered as late as 10,000', and likely much lower (the attempt when they started realizing their fate at 4000' would have been close, but maybe possible).
As for the "Hail Mary" system, it would depend on what input that system used. The combination of AOA and pitch attitude may have allowed an automatic correction even without airspeed, but any system that depended on airspeed might have failed.