However maintaining a constant back focus they could "region" the sensor to FF and you could use existing FF lenses.
I suspect you would have the same problems with FF lenses on an MF body that you'd have with EF-S lenses on a FF body. They're designed under the assumption that the mirror will be a particular size, and MF would require a bigger mirror. Judging by the very small difference between adapted lenses that hang at infinity and Canon lenses that don't, I suspect that a change in mirror height of only a millimeter or two would be enough to cause problems.
You could work around this with a specially designed teleconverter attachment that spreads and refocuses the light over the larger surface, with a mirror that doesn't flip straight up, or with a mirrorless design, of course, but each approach has disadvantages, either in IQ, battery life, or mechanical complexity.