Can a man and a women be married in the eyes of god without a marriage license?
Yes, if you live on a deserted island!
The Bible exhorts Christians to be subject to the governing authorities (Romans 13:1-7). Jesus said, “give to Caesar what is Caesar’s” (Luke 20:25). The government requires a marriage license for a man and a woman to be wed. If a man and a woman choose to live together the government still gets involved by declaring that they are married by common law even though they did not have a ceremony or a certificate. You cannot escape the government or God on this issue. “Everyone must submit himself to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God” (Romans 13:1, NIV).
I believe that a marriage ceremony and a license are good things. They are public matters. Jesus Himself attended a wedding, thus endorsing the marriage ceremony. A marriage ceremony complete with a license shows respect for God, for government, and for society. Christian marriage seeks the blessing of all three on their union. Why would a couple not desire this?
Frankly, a license for marriage helps to maintain an orderly society. When people do whatever they think is right in their own eyes bad things happen (Judges 17:6; Isaiah 5:21). Our culture has a hard time with commitment. A marriage ceremony and a marriage license elevate the importance of commitment to the family. Without stable families led by a man and wife that are committed to each other, society crumbles.
For a more detailed examination of your question see Seven Reasons Why God Created Marriage by James Ford, Jr. and Why Marriage Matters: Reasons to Believe in Marriage in a Postmodern Society by Glenn T. Stanton.
~ Pastor Chris