Double ring ceremony

Question

I apologize for sending this several times, but i have yet to receive a response so perhaps it was missent. If a woman marries with a double ring ceremony, and while the man says nothing under the chupah, but the ceremony is meant to be an exchange of rings, is the kiddushin valid? Does it matter if the woman divorces, and then wishes to marry a Kohen. (i.e. is there a reason to be makhil in that circumstance)