One of the first things I was taught in primary training is, "Don't trim into a stall." Apparently, the AB system will do just that in some circumstances.
That is why on all our recurrent training sessions we go through 4 types of stall exercises and they are done all with the AP on so that you do get a nose high trim situation because the AP will trim until the shaker is activated.
Stall exercise #1: 10,000 feet, clean, then slats out only, then slats + flaps at the two takeoff settings, then slats + full flap. One of these will also be done with a continuous 20 degree bank turn.
Stall exercise #2: Low altitude stall in a landing configuration (full flaps), again with the AP on. While levelling off on an approach at the MDA (400' AGL), the trust levers are brought back to idle where they stay until stick shaker/AP disconnect.
Stall exercise #3: High altitude (high 30s) with a heavy aircraft.
Stall exercise #4: Takeoff with an engine failure with a climbing turn. The AP is selected on at the proper altitude and a 15 degree bank continuous turn is initiated using the VS mode and set a high rate of climb until stick shaker/AP disconnect and recover.