The answer is "maybe", superglued and sinew backed I wouldn't expect a problem but if you can get rid of the drying checks by going down a ring I would.
About 25 years ago I put a nice stave behind a water heater that was sitting in the corner to dry it out a bit more. It checked much like your stave did. I learned the same lesson by putting a stave in a hot car and hot attic to speed up drying, bad idea.