Can you put stoneware on a wood-burning stove as a steamer?

Yes. Good idea ! Our homestead cabin always had a copper-bottomed pot full of water ( snow or ice in winter ) on the wood-burning stove in order to constantly humidify the dry air from the intense wood heat.

Stoneware is much more durable than pot which was still usable after about 15 years of being heated and kept hot. Caution - always top it up before going to bed so that you don't damage container by boiling it dry.