question: On the NG does the AP automatically disconnect at stick shaker?
737 AMM 22-11-00-146 (DFCS Functional Description)
Engage and Disengage Functions 24. The signal from the SMYD that shows a stall condition and activates the stick shaker must not be active.
So the answer to your question is yes; if the pilots had not yet pushed the control yoke forward, the autopilot is supposed to disengage when a stick shaker is activated by the SMYD.