As for Common Law Marriage:
In Alabama and Texas, and a couple of other States that I know of......Common Law Marriage is legal. Two people (man and woman.....to be clear) who "represent themselves" to the world as being married.......ARE! In other words, if they live together, introduce themselves as husband and wife to the public, and live as husband and wife........they are legally married. And, it requires a Legal Divorce through the Court System to dissolve their union.
Now, as for God.........I think there could be an argument made that two people who do the same thing in full knowledge of God and His Word, and live as man and wife may well be considered married by God. It may well be possible that, for one reason or another, they can not get a Marriage License, and have a legal Ceremony preformed. It's the same as two people being married by a Minister without the Civil License issued by the State. They were married by a Minister of God...........so, would God consider them married? I think so.
Then, of course, just to confuse things, we are told to honor the laws of Caesar for the glory of God.............. soooo