OK, in the interest of science
I took a Barbie apart and put both her body and head in the oven at 300F (the highest temp I think anyone would be baking polymer clay) - at the end of 5 min. everything looked fine. However, at the end of 20 min., surprise! head still looked fine, if maybe a little soft, but -- the body was melted.
So there we have it, friends and neighbors - you can't bake PC embellishments right on Barbie. I think I may just mold the piece to the doll to get the positioning right and then remove it and use some sort of support to hold the piece in the same position.