I have a question about FBW/sidestick aircraft (for someone that has actually flown one, please): When the autopilot is engaged, can you feel or see the stick move while the AP is flying (like in a conventional control setup), or is the stick stationary as if it were a computer game joystick?

If the stick stays "dead" during AP operations, this would bug me. In a conventional control aircraft, you can leave a hand on the yoke and feel what the AP is doing and still have some connection to the status of the aircraft, like in turbulence or on a coupled approach.