Only for zooms and only for the full wide and full tele positions. No guarantee that an extrapolated AFMA will work for in between values. However because your DOF is deeper at wide angles it's "less" important as at full tele.
So depending on how far off the AFMA is through the range, you might be able to get away with using an AFMA value for the wide setting that is more in tune with one of your most used MID ranges and let DOF mask the error wide open.
Depends a lot on the lens and how far off the AFMA is through the zoom range. If the AFMA swings wildly through the zoom range it might not be possible to fudge the AFMA.
So you can have 2 AFMA values for one lens on the 5DMKIII? For wide and tele?