I'll give you an example one of my friend, she is a Muslim married to Christian and she marries him under Sharia law, he never converted and they brought up their children as Christian and the husband and her children goes to church every Sunday but not her. So in other words, it is allowed for the Muslim woman to marry a Christian man. And yes its also possible for her to divorce him simply because they are married under Sharia law and they do have divorce.
And to answer your question if they get married in the church, that can be null and void later on! sometimes some people get married in the church even one party is catholic but they don't really declare the truth about the other party's religion, if time comes they don't want to be together anymore this is one of the technicality they use in order to get out of marriage.