To all,
A stick pusher is normally added to an aircraft if it displays some behavior during the stall, that deviates from the benign behavior of consistently dropping the nose wings level. It's not uncommon to add it to an upgraded version of an aircraft, when more powerful turboprop engines (more powerful than the original design) cause some new disruption of airflow over the wing during a stall, resulting in one wing dropping more that the other in the stall. So the need for a stick pusher may not be related to deep stall at all, however since a wing drop during a stall could result in a spin, the stick pusher is used to prevent the stall in the first place.
I don't know why the stick pusher is used on the Q400, but again, it's normally used to mitigate some less than benign stall characteristic.
Edited to add:
I found this old article from Flight Global in 2000 (a pdf photocopy of the then magazine article), explaining the stall characteristics of the Q400, and the need for the stick pusher. The aircraft indeed has some "propeller effect" from the new engines. In fact this link has an entire flight test article for the Q400. Just click on the magazine pages to the left, to see the other pages.
stick pusher | roll control | stall | 2000 | 1351 | Flight Archive