No. When you apply full forward stick you get full elevator travel, at least until the lower G limit of -1 is reached. If you manually move the trim wheel, automatic stabiliser trimming stops for a period of time. Hence, a little nose down stab trim can be a bad thing if the pilot then subconciously is relying on the FBW to complete the THS nose down travel.
In the very high AOA cases they claim there is no valid data set upon which to build a sim model. Yet Airbus used a sim to model the AF447 flight. From that experience they changed the stall recovery to include the selection of flaps one below FL210, the goal being to extend slats, thereby decreasing the net angle of attack. They also noted an improved stall recovery with manual stab trim, exactly as in almost every modern transport jet.
We used to go decades without hearing of a stall accident. Now it seems to be weeks. What gives?