Seriously?
OK, true, if you are in a climb; but is it that critical? However, and I've seen it in the sim many times, they get a 'CLB CLB RA"; disconnect everything, apply 3g pull and forget to add power. Now do that at FL350 and see what the speed does. Is a low speed more/less critical than overspeed? One has a clacker the other a shaker & clacker. I've also seen the "DESC NOW RA + Increase ROD". Then "Clear of Conflict" = climb back to last cleared FL and forget to add thrust. Consequence? see above. IMHO on there balance of risks I'd rather keep AT engaged. Dogmatic philosophy has its weaknesses.
There are no TCAS manouvers that require a 3 G pull. A manouve like that at FL 330 will be interesting, with or without thrust. It would be a FAIL and retake in my airline.
ANU = more thrust. Pretty basic, so if you many times have seen pilots who fail to understand this, then I suggest you may have a problem on your hands.
Maybe you should transfer them to Airbus?