I am not sure what planes you actually fly but our club as 182's and 210's with autopilots. The trim wheel in those planes is mechanical. When you turn the STec autopilot on it will make a reasonable attempt to trim the plane using the elevators because that is all that the autopilot is attached to ... it is not attached to the trim mechanism. If it can not successfully trim the plane within its definition of "reasonableness" then it will turn on lights and a buzzer which suggest to the pilot either turn the trim wheel up or down to bring the plane within the autoplots "can reasonably trim the plane with the elevators" envelope. What all that means is that the autopilot does not actually change anything related to the trim wheel and when you turn the autopilot off you can expect the plane to assume whatever trim configuraton is defined by the trim setting. I've never experienced "huge putch inputs" in real life but I do expect I may have to retrim after turning the autopilot off. My experience also suggest that the autopilots "reasonableness envelope" is pretty small so the plane is never very far out of mechanical trim before the light and buzzer come on telling you to change the mechanical trim.
