As long as the decorative side isn’t affected, it should be fine (and that’s only an esthetic thing anyway).
Just clean it up and try to get as much residue out of the back as you can. The easiest thing to do is just throw out the whole clock mechanism and replace it (very, very easy), but if you don’t want to do that, and the mechanism itself isn’t affected, you could probably just buy a new battery enclosure with the same battery capacity as the original, and wire it to the same connections the original batteries had.