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: http://camerasize.com/compact/#487,351,325,466,459,ha,f
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!