If a couple consists of two divorced individuals, and they are converted to Christ and are baptized, do they need to separate?
This question leaves out too much to answer well. For example, you did not mention whether the individuals had a right to remarry. The Bible speaks of divorced people who have no right to remarriage: "Now to the married I command, yet not I but the Lord: A wife is not to depart from her husband. But even if she does depart, let her remain unmarried or be reconciled to her husband. And a husband is not to divorce his wife" (I Corinthians 7:10-11). Yet, at the same time Jesus implies that a person who divorces his spouse due to fornication on his spouse's part can remarry without committing adultery: "And I say to you, whoever divorces his wife, except for sexual immorality, and marries another, commits adultery; and whoever marries her who is divorced commits adultery" (Matthew 19:9).
If a person is actively engaged in sin, the act of baptism does not change a sinful action into a righteous one. If a thief decides to be baptized, it doesn't mean his stealing is now approved of by God. In the same way, the act of adultery is not a one time event. A person living in adultery before baptism would still be adultery after baptism.
But there is a more fundamental point that is being ignored. In order to become a Christian one doesn't simply get baptized. God tells us that there are several things that must be done, such as hearing the word, faith, and confession. But not least is repentance. "I tell you, no; but unless you repent you will all likewise perish" (Luke 13:3). In your scenario you are describing a couple who were baptized without repenting of their adultery (assuming one or both had no right to remarry). How can a person be saved if they refuse to repent of their sins? "Then Peter said to them, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit"" (Acts 2:38). Baptism without repentance is as useless as baptism without faith. If this couple needed to separate because of an adulterous relationship, it must take place before baptism, not after.