@LW_50:
The infamous A320 video illustrates the point here. With insufficient thrust/speed to climb, the aircraft's systems hold Alpha Max.
Capt. Asseline asserted correctly that the aircraft would not allow him to climb, but the investigation discovered that this was due to the reasons above (i.e insufficient airspeed due to A/THR disengage and poor approach technique), proving in the process that Landing Mode was not triggered.