Just thinking out loud here, buy you could round off or shape the END of a stone with a coarse diamond plate to the desired radius of a concave grind, lock the stone handle in place and do sweeps only along the blade’s edge. I wouldn’t recommend the effort however as ultimately the ANGLE at the edge of the edge is the critical parameter and you would get an unnecessarily delicate edge. You are ultimately limited in how acute the final edge is on your blade by the steel’s capacity to take an acute edge. For concave grinds the opposite side of the concavity limits the sharpening angle unless the abrasive surface is round / convex, like a grinding wheel. And here, you would ideally want a wheel of the same diameter as the radii of the concave surface.
If you look at a traditional Japanese Straight razor (kamasori), it has two concave sides, yet the final bevels are ground flat on both sides. Same with Western style straight razors. It is a pretty firmly established concept. This is also true with concave ground pocket knives, eg a Jess Horn Spyderco ZDP-189 blade or a Gayle Bradley Spyderco CPM-M4 blade.
For a Japanese traditional single bevel kitchen knife the back of the blade is also hollow ground. But this hollow back or urasaki is ALSO ground flat along the rim of the concavity. There is a pattern here in how one handles a concave shaped blade with a flat grind for the final edge. Same with Japanese chisels too.
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Ken
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