NOOOOOOOO! Gentle hand cleaning on those babies. I don't think it would make a meer explode or anything, but owing to the delicate nature of the clay, and going by all I've heard, I would say no (unless Fred or someone has other advice?).
I won't even put water in my meers. Just a paper towel, or microfiber towel every so often.
The stem will get an alcohol soaked pipe cleaner from time to time, but nothing much else from there.