Well, I thought so too, but changed my mind after looking at Owain Glyndwr's data. With Owain's help I did a similar analysis and got similar results shown in the graphs below. The second graph shows how AoA slowly reduces until the airplane is unstalled.
I'm glad we are bringing up this subject again. Pointing the nose below the horizon adds effective thrust along the aircraft axis in the amount of sine(negative pitch angle) x weight of the aircraft. In effect you are powering out of the stall with sufficient power to let the aircraft accelerate despite the high induced drag.
This probably isn't the most efficient way to get an airliner out of a stall, but for one that does not have an AOA indicator, it has a lot to recommend it in that the likelihood of secondary stall is drastically reduced. You just have to get the nose low enough initially so that you can actually accelerate. Surprisingly, angles of as little as 10-15 degrees nose low seem to be sufficient for the A330 to accelerate, despite having a very high initial AOA.
In the military aircraft I've flown, we were always concerned with departures from controlled flight (spins), thus the importance of unloading the wing promptly before you began to generate unintended rates of yaw/roll.
With an aircraft that is (relatively) stable in the stall, you just have to avoid doing something stupid with the controls.
I hope someone (like NASA) does further study on this method of stall recovery.