The yaw damper is installed to prevent Dutch roll. So even in turbulence there should be no Dutch roll. There is no Mach trim in the 727. With a Mach limit of .90 I don't know what the critical Mach number is. And Mach tuck isn't much of a problem until you get close to critical Mach.
Been through many of the drills OBD mentions. I've seen them get out of hand if the pilot got out of sync with the ailerons. Like the old method of stall recovery (not losing altitude) it shows you can fly the plane. In the real world if you have a yaw damper failure you are going to have to slow down and go down so close the thrust levers, pull the boards and request a descent.