Is there any obvious warning when auto-pilot is disengaged or when the mode changes?
The Boeing 737 allows a mode called control wheel steering (CWS). The A320 doesn't. For what is CWS, see: Is it possible to disengage only one axis of a two-axis autopilot?

The wording on Wikipedia doesn't emphasize this point; however, the final report does.


  The pilots may also manually control the aircraft in a normal manner with the control wheel and column (control wheel steering [CWS]) without disengaging the pitch or roll axes of the autopilot system. Pilots can then assist the autopilot system in flying to a selected heading or course. Use of CWS does not disengage either channel of the autopilot system. The autopilot system was modified from the original design to allow for the use of GPS guidance for the course signals to the autopilot (section 1.6.10).


Note that Wikipedia says "(...) disengage from VOR/LOC mode (...)".


Therefore, for First Air Flight 6560, the autopilot was not disengaged.
Switching to CWS is not aurally annunciated. See also: Why are callouts of changes in the Flight Mode Annunciator not automated?
Autopilot disengagement is accompanied with aural and visual warnings. See: Why is an auditory alarm necessary when the autopilot disengages?




(All bold emphasis mine.)