LEM, take care with any assumptions that you make in the use of the “Autopilot Disengage Bar”.
I suspect that the 737 is very similar to, if not the same as the Avro RJ autopilot engage panel (the RJ has a Honeywell design based on 737). The RJ Disengage Bar is specifically an “emergency” disengagement system for use in the event of the normal methods failing. Thus, the bar has no involvement in either normal engagement or disengagement and should remain up at all times. If the bar is down in the RJ there is a red / black stripped warning to indicate the bar’s abnormal position and I recall that a down selection sets a maintenance fault.
Also, disengaging the autopilot with the bar in the RJ, invokes different functions. So that if the control-wheel disengage buttons fail or the autopilot computer rejects that input, then the bar will by-pass the normal operation and cuts engagement power the autos. This action, from memory, also removes power from the controlling pitch, roll, and yaw servos, although I think not for pitch trim or yaw damper – Avro RJ operators check the manuals.
The Avro RJ has engagement buttons in lieu of ‘paddles’, but their use differs from the 737’s selection of A or B channel (or similar, I don’t recall), in that the RJ has a single (integrated dual lane) autopilot where the buttons switch between sensor inputs – Nav 1 / Nav 2.