Anything left attached to the guitar for long periods will cause some fun, that could be called damage.
UV exposure darkens wood with time, so if you keep it on your guitar all the time, when removed there will likely be a light spot where the wood was sheilded from the UV. If you keep your guitar in a sunny room this can happen fairly quick depending on the wood and if the finish on the guitar has any sort of UV sheilding in it.
The one iffy area is if you use a cleaner containing any solvants on your guitar then stick the tuner on it before the solvant has fulley evaporated off, it will affect the foam padding and could make it go gooey then harden and sick, perhaps pulling finish off when removed. You see this on old old foams. with time they turn gooey from all the random things they slowly absorb. But it can happen quite quickly with they right solvant
Just take it off right when you are done tuning and you will most likely be safe,
P.S. Tuning fork.