No matter what warnings and protections are built into one's plane, complacency can kill you.
This has happened on Douglas, Boeing and even Airbus machines.
A B-757 crew rushed themselves during a typically steep descent and left a charted arrival route in the Andes Mountains. When they were very surprised by the GPWS warning and went to Max Thrust (!), they forgot to retract the speedbrakes. It is easy to forget that they are out in the 757 (they often make no vibration or noise), and crews use them VERY often (SFO/..LAX...ehm.../SEA/DTW/MCO/LGA....).
Even an Airbus factory demonstration pilot at Toulouse pulled one throttle back on an A-330 (with two Italian pilots watching from the jumpseats) and with an autopilot engaged, allowed the plane to quickly climb at a very high "deck angle' and then it stalled/crashed. The main point is that he allowed the autopilot to be 'in command', until much too late. I've never trained on any Airbus, but know lots of guys (a few gals) who fly them.
If anything makes you or the other pilot(s) uncomfortable, switch the autopilot(s) or autothrottles off (did he say that?!) and re-engage the autopilot/flight director system, or whatever you need to do.
Any half-decent training department will give you some exposure to hand-flying any plane without automation being required, in order to get you onto downwind, base then final approach .
