Will car polish remove a ceramic coating?

A car polish will remove a ceramic coating, but very slowly. Car polishes are usually abrasive compounds in order to remove soft, oxidized paint, they are like a very fine liquid sandpaper. Therefore, they will abrade the ceramic coating, even though the ceramic coating is very tough and harder than the abrasive compounds.

There is no need to polish a ceramic coating because it is extremely resistant to oxidization and won't need polishing. Should your ceramic coating get scratched, seek the help of a professional who can use machine polish the area using aggressive polishing compounds to remove the scratches, and afterwards re-apply ceramic coating.