Will polishing over a ceramic coating remove scratches?

Depending on the severity of the scratches, yes it will.

However, a ceramic coating makes your paintwork extremely tough, which will help resist scratches in the first place, but it also means it resists polishing. This makes polishing hard work, even with machine polishers. Hand polishing really isn't an option, as this is only really good for removing dead paint and does little for removing scratches.

Scratches that have penetrated too deep cannot be polished out, regardless of if you have had a ceramic coating or not.

If you have a car with a semi-permanent coating, and you are concerned about scratches, you should seek the help of a professional so that the problem can be diagnosed and corrected.