In a fixed gear aeroplane, unless you can see the gear, including undercarriage in a checklist is bad training. All that is accomplished is that the student is trained to say the words without checking anything.
Far better to teach the use of undercarriage to control speed during the approach. Checklists, pre-determined points for lowering and warning systems are secondary defences. The primary defences should be, 'I need to slow down so I'll use the gear', or, 'I'm going faster than I normally would be for this situation, I should check the gear'.
The repeated reference to CAR 138 is quite boring. Nothing therein prevents items additional to the AFM unless also conflicting with the AFM, which I believe is the point of the thread.