With over 1000 hrs on the Dominie (HS 125) I can state with certainty that it did NOT have a stick-push system.
We regularly stalled the aircraft clean but only went to the calculated stick shaker speed / actual stick shaker (whichever was the higher) in the Approach Configuration - Gear and Approach Flap.
There was some discussion from Multi Engined Standards Sqn that a fully developed approach stall would be quite nasty.