I think the general consensus (in this post) on fired clay was no, BUT if the ingredients in your clay are safe to laser, give it a shot.
People have had success with etching on ceramic tiles, such that it burns away the glaze. I don’t know what kind of glaze is on there, though, and how thin it would need to be. Seems like a fun thing to play with.
I’ve been enjoying using patterned stamps to make pendants, so yeah, it would be fun to be able to etch those.
You might like to see this, too. One of the women at my maker space (who now own her own pottery studio) engraves bats on her laser that she uses to add decorative touches to her pottery. https://www.potterymill.com/flexi-bats