Not sure this can even be answered yet but if Canon came out with a full frame EOS-M version, would they need to change to a new lens mount as well? Could the EF-M still be used?
EF- M mount can't be used for FF unfortunately. Too small. Likely they'd create a mirrorless camera with the regular EF mount instead.
This is widely stated, but I can't see that the EF-M mount is much different in dimensions to the Sony E mount; I know that E mount is tight for full frame, but it is still possible. I'm struggling to find the technical specifications, but here's a comparison (assuming the scaling is correct) -measure for yourself:
EF-M is pretty similar to E-mount in its internal diameter and a bit larger than either X-mount or micro 4/3rds. We also know that the flange back distance is the same as E-mount (18mm, vs 44mm for regular EF).
I'm not saying that this proves EF-M is compatible with full frame sensors, nor that Canon would have any near term plans to produce a full frame mirrorless camera if it were, but it would be a bit strange if they happened to make it so similar in size to E-mount and it not be FF capable. They must have had some idea that Sony were interested in making a FF E-mount camera. I believe that FF probably is possible with EF-M mount, if nothing else then to cover that base for the future. Of course, Canon would never admit that now whilst it is still trying to push their FF DSLRs!
As for a mirrorless camera with an EF mount: it's possible but not with a reduced flange back distance, or they'd create all sorts of lens compatibility confusion!
According to Canon's full frame white paper, the diagonal measurement of a FF sensor is 43.3mm The measured inner diameter of the lens mount opening on the EOS M, accounting for the bayonet protrusions, is 43mm. For comparison, the measured inner diameter for the EF mount opening is 51mm.
Having said that, the Sony a7 mount opening appears to 'clip the corners' of the sensor, and is quite similar in size to the EOS M's opening.