Ah yes, but in the US it is illegal for a priest/pastor to perform a wedding withoug a marriage license. In parts outside the US this is not true.
It is the way my wife and I would have preferred it to improve tax and other legal money matters.
We wanted to be married in the eyes of God, but not the state.
It is not illegal to perform the ceremony without the license. It is just the marriage will not be recorded or recognized. The children will be "bastards" in the eyes of the law and all issues of paternity will have to be constantly proven.
HOWEVER if you live in a state which recognizes common law marriage you will be married. Also you will be married EVEN IF YOUR STATE DOES NOT HAVE COMMON LAW MARRAIGE because the state will recognize a marriage from a common law state for purposes of marraige.
Thus documenting the ceremony abroad will still put you in divorce court AS IF YOU HAD A LICENSE in the USA.
So your cleverness only gets you a bigger mess and a larger lawyer fee.