I don't think so. I am not saying that people who do not believe in God cannot be married, and that their marriage does not have meaning to them but...
Our pattern for marriage comes from God. I don't believe you can fully understand marriage unless you know God. The Bible likens our faith in Jesus Christ as a marriage where He is the bride groom and we (those who believe, the church) are the bride. And just as we are to become people of God and leave this world behind (I am speaking of worldly desires) a woman leaves her family and becomes part of her husband.
Looking at it in other ways... God created the universe, but why? He created man, saw that man needed a companion and created woman. But He desired a more intimate relationship with us, coming into the world as a man. I ramble, I know, but the point is that God himself desires a companion: us. And all things good flow down from God, as does marriage. It's a sacred bond, but one that is freely chosen by both parties, to commit to one another, to care for one another, to be friends and more.
