Stall phenomena are covered during the initial A320 type rating,
and
Note: Stall and stall recovery exercises are undertaken during initial pilot training (in particular basic training, private pilot, professional pilot, etc.) but not during type rating training.
Seems they can't
both be true.
Further more the tendency of the flight control law to want to pitch down at stall would be dependent on if the low-speed stabilities were active while in Alternate law, which in AF447's case, they were not (due to lack of IAS). So unlike the α-prot (aoa command) in normal law, or when the low-speed stabiliites are active, the pitch command was still centered on g-load/pitch rate (aka C*). I believe you can see the elevator response (up) to the g load going below 1 as the stall progresses and the airplane starts to accelerate downward. This requires pilot action - stick forward - for as long as it takes to get the nose to drop and the aoa to reduce. I also found that in the simulator manual forward trim was required, as even a full down elevator was not enough to counteract a full up stab as airspeed started to recover.