Or depends?
Generally if you have a fixed position rest tuned properly then install a WB so the arrow is in the exact windage and elevation location as it was on the fixed rest, the bow should remain tuned.
I think I've got one of those false tunes Len brings up about the WB going on, and am grasping at straws on how to correct it if at all possible. My center shot is WAY left of where it was previously, yet I'm getting bullet holes from 6'-20 yards.
Any thoughts?