Yes, probably depends on the control system. For what it's worth, the yoke in a Boeing 737 does move with its electrical trim movement. It moves very slowly, but the entire trim system moves very slowly, and it takes a loooong time to move trim from one end to the other. Other experiences from me are all the 20 or so types of gliders I have flown have moved the stick quite a lot with trim change. They are using spring type of trim. I have flown some powerplanes with sprint type of trim and they also move stick position, but others with other trim systems I have not flown enough to pay attention to stick movement with trim.