ames: it’s a huge machlokes. Some Rabbonim hold it’s completely assur. Some hold it’s allowed, but you should have a non-Jew carry the pregnancy, and do a geirus right after birth. It’s a big machlokes, again, whether the child takes its Jewish status from the genetic mother, or the woman who carried the pregnancy. So, to be certain, you do a conversion. At Bar/Bat Mitzvah age, the child does not get to choose whether to stay Jewish or not, as it was only done to be certain the child is Jewish. I don’t know how it relates to marrying kohanim.
Again, as always, ASK YOUR RAV!