Can I clay bar a ceramic-coated car?

Yes, but only when bonded contamination remains after washing and chemical decontamination. Clay works through mechanical contact, so it can reduce slickness, introduce fine scratches or weaken the top layer of an existing coating. Use plenty of lubricant, a fine-grade clay or synthetic clay medium and very light pressure, and treat it as an occasional corrective step rather than part of routine maintenance. Clay does not strip an entire coating in one go, but aggressive grades, heavy pressure and repeated passes wear it down; a compatible topper afterward can restore some of the lost slickness.