Can a ceramic coating be removed?

Yes, but not with ordinary washing. The reliable way is machine polishing. Chemical strippers and strong cleaners can remove toppers and contamination, but a cured ceramic coating is designed to resist chemicals, so polishing is normally needed to take it off. In practice, the paint correction step before recoating removes the old coating at the same time. After polishing, use a panel wipe to remove residue, then check water behavior: a panel that still beads strongly may still have coating on it.