I don't have an auto-pilot, but I do have a question.... How can you trim with the AP engaged? It would be like you, the pilot, trimming while the co-pilot is trying to keep the aircraft level.
Exactly. And this is how autopilots have worked for decades (unless they have autotrim capability). The autopilot doesn't have any idea *what* is causing the aerodynamic force that is pushing it off of the setpoint (or outside the deadband). Could be a trim tab, could be the pilot or copilot pushing on the stick, could be a gust of wind, could be a change in power setting...all it "knows" is that the airplane is deviating from the setpoint, and it needs to send the signal to the servo to move the control surface to correct back to the setpoint.