I wouldn't want to use any paints that would inhibit the nice breathing quality that makes clay so beneficial. I don't see why it wouldn't work as well as plastic pots though. Several house plants, trees really, my family raised lived over 20 years in clay Terra pots! They were root bound, one a palm over twenty feet tall in it's original pot.
IMHO, if it's something that YOU like, that's what matters most.
There's special plastic primer and paints for plastic. It still might require sanding prep to stick though and yearly redo.
I Did that with shallow hard plastic pools. Looked good at first. Snooty Neighbors who never planted more than dandelions complained. Dog walkers, (like walking dead walkers), through new plants ruining hundreds of $ worth of landscaping even complained. What a neighborhood. Not just zombies....No. RUDE entitled zombies.
Solution...Fabric store. The plant Manufacturer's Father made sure that a nice light Moss green was set aside and marked on clearance for me. It was low fade polyester and has been out in direct sun and the elements for around a year. Still looks good! Wish I had pictures. It really sets off my landscaping. My snooty neighbors got so mad.😆LOL! I'M not competing with the Jones's. They just don't like it when I get new plants and get it right. They even swarmed me while I was pulling weeds one day! Zombies???No. Grown men. Hahahaha!
That said, you may be wondering how to attach it?