I suppose it depends on whether rote learned checklists count as being "carried in the aircraft" and "located where they will be available instantly to" the PVT pilot. If the pilot's head is in the aircraft, and the pilot's head contains the checklists established by the operator and the pilot can recall them instantly, I don't see why that shouldn't be enough.
I suppose we'll find out CASA's opinion on the question, the next time they ramp check a PVT flight and ask for written or electronic copies of checklists in accordance with ramp check guidance, and the pilot says: "It's all in my head!"