Supposing that all other variables are such that you would be willing to officiate a particular couple's wedding....
Suppose they said they didn't believe the state should be involved in weddings and they didn't care about the state recognizing their wedding; they just want to be married in the eyes of God and the Church. Therefore, they choose to not apply for a marriage license. Would you still officiate their wedding and proclaim them husband and wife? (Even though the state will not recognize them as husband and wife...)
(If some of you non-pastors want to get in on this go ahead and pretend you are a pastor for the purposes of this thread! However, please remind us that you are not a pastor: "I'm not a pastor, but...")