Do GA pilots have/ use/ are disciplined in such mandatory memory items?
Well since "GA" covers most if not all flying which isn't part 121 airline or military, answers may vary among different segments of GA.
I can say with assurance that the part 135 jet charter segment trains loss of pressurization scenarios at each simulator training event, at least in my own experience. It was definitely specified in the last part 142 training center agreement I reviewed in it's entirety. As per our approved company training program of course. This was for my last part 135.293/297 recurrent training and checking event. I know it's included in type rating training for non air-carrier bizjet and turboprop pilots too.
Since the TBM is a light prop airplane and does not require a type rating, then the training and endorsement required by 61.31(g) (one-time) may be the only "hard" regulatory requirement. However I find it highly unlikely that any part 142 simulator training center would leave it out of an initial or recurrent simulator training event. Pilots/owners of such aircraft may find their insurance carriers "encourage"
their insured to partake of such training as well. Or so I've been told by more than one owner of a high altitude turboprop.
westhawk