Nope. I see nothing about a minimum cohabitation period in any state where it is legal. Also, look at Kansas and particularly South Carolina below. There is nothing magic about a ceremonial marriage vs. common law, where the law permits such.
STATE-BY-STATE REQUIREMENTS TO FORM A COMMON LAW MARRIAGE:*
Alabama: The requirements for a common-law marriage are: (1) capacity; (2) an agreement to be husband and wife; and (3) consummation of the marital relationship.
Colorado: A common-law marriage may be established by proving cohabitation and a reputation of being married.
Iowa: The requirements for a common-law marriage are: (1) intent and agreement to be married; (2) continuous cohabitation; and (3) public declarations that the parties are husband and wife.
Kansas: For a man and woman to form a common-law marriage, they must: (1) have the mental capacity to marry; (2) agree to be married at the present time; and (3) represent to the public that they are married.
Montana: The requirements for a common-law marriage are: (1) capacity to consent to the marriage; (2) an agreement to be married; (3) cohabitation; and (4) a reputation of being married.
Oklahoma: To establish a common-law marriage, a man and woman must (1) be competent; (2) agree to enter into a marriage relationship; and (3) cohabit.
Pennsylvania: A common-law marriage was established if, before 1/1/2005, a man and woman exchanged words that indicated that they intended to be married at the present time and they also held themselves out to the community as married (introducing eachother as husband and wife, filing joint taxes, etc.).
Rhode Island: The requirements for a common-law marriage are: (1) serious intent to be married and (2) conduct that leads to a reasonable belief in the community that the man and woman are married.
South Carolina: A common-law marriage is established if a man and woman intend for others to believe they are married.
Texas: A man and woman who want to establish a common-law marriage must sign a form provided by the county clerk. In addition, they must (1) agree to be married, (2) cohabit, and (3) represent to others that they are married.
Utah: For a common-law marriage, a man and woman must (1) be capable of giving consent and getting married; (2) cohabit; and (3) have a reputation of being husband and wife.
Washington, D.C.: The requirements for a common-law marriage are: (1) an express, present intent to D.C. be married and (2) cohabitation.