Owain... At last, a bit of good news. A contributing fault identified and the answer to the title of this topic. YES IT CAN!
By all accounts the magneto is generating sparks but not necessarily at the right time, and the reason why is now clear. Looking back at this saga, the answer was there from the start.
So for now I would clean up the mating surfaces, even a vestige of the key should be enough to locate it. If it is smoothed off completely try a small drilling and a soft brass or copper locating peg. Just big enough to locate the plate, but not too big to bottom on the internal slot on the armature taper. As groily says, the drive is transmitted by the taper, and the bolt needs to be reasonably tight for the taper to grip, but not murder tight. Tapers too loosely tightened are the main cause of keyway damage and sheared keys, typically as seen on gearbox mainshaft/clutch centre tapers.
Another problem may be that the internal taper on the armature has been spread, resulting in rock on the points plate, and consequent inconsistent points gap (and varied timing) between the cylinders.
What I am suggesting is to reassemble with what you have to establish whether the magneto is capable of sparking at the right time, before spending more cash on what may prove to be a shagged armature. A bit of a temporary and maybe unreliable fix, but to just get it running again. For future serious use I still consider a Thorspark System is your cheapest long term option. You may spend up to 25% of this cost just for a set of well used points on a questionable backing plate.
Brass contact plates and later steel backed versions interchange, but each requires its own specific retaining bolt.
Swarfy.