Church marriage without civil marriage?

Question from Adrian on 2/13/2008:  
Not every civil marriage is a Church marriage. This much is obvious. But, is every Church marriage automatically a civil marriage?

Why would I ask? Well, I am a US Permanent Resident (green card holder) who would like to marry a foreign student (who is here on a student visa). Because of immigration regulations and waiting lists, this is a complicated process which could take years to complete. But, since we can do without the civil benefits of a civil marriage, I wonder if it would be possible to have a Church marriage now, to be followed by a civil ceremony some years in the future.

I understand that the priest at a Church wedding acts as a witness for the Church and the State, but is it possible for him to act as a witness for the Church alone if those to be married are not seeking State recognition?

Thanks for providing this Q&A service. It is greatly appreciated.
Answer by Fr. Jay Toborowsky on 2/14/2008: 
As far as I know (and as far as I have been taught), clergy in the United States must have a civil marriage license before they will marry a couple. Now, Canon Law does allow for what are called "secret marriages" whereby the marriage is recorded by the Church but not recorded in any government records. But these are rare exceptions done, not for the couple's sake, but for the clergyman's sake in places where there might be persecution of the Church. The bottom line is that, in the United States, you cannot have a Church marriage without it being recognized by the civil government.