Dear Catholic Warrior...
Q. "Is it a sin to have intercourse with a woman and being only secularly married to another at the same time who does not live with him? Suppose the married couple does not have children."
A. The short form of this answer is simply put that yes it would be a sin. Let me explain. Jesus in the Bible said: "I say to you, whoever divorces his wife (unless the marriage is unlawful) and marries another commits adultery." Then again in the Bible it says in I Corinthians 6:9: "Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived; neither the immoral, nor idolaters, nor adulterers, nor homosexuals, nor thieves, nor the greedy, nor drunkards, nor revilers, nor robbers will inherit the kingdom of God."
I underlined "adulterers" to point out how this is saying that those who commit this sin will not enter Heaven unless they repent of their sin. From the information you have given me I must assume that this woman is married to this man, and although she may be separated from her husband at present, in God's eyes they are still married.
Also, our belief based on the Bible and the Church's teachings (God's teachings) that sexual relations before marriage is gravely wrong is true. Sexuality is only for those who are validly married because sexuality is not only for the closeness of the married people but also for the creation of the family. It is something sacred and should not be used outside of God's boundaries. Sexual relations outside of marriage is considered grave matter and would be a mortal sin. See the Catechism of the Catholic Church #2353.
You may believe however that this woman's previous marriage was invalid as it may have been one outside the Church and outside any sacramental institution. However, you need to talk to a trustworthy priest and get a hold of a canon lawyer if you have questions on whether the marriage is/was valid. Remember though that marriage is sacred and that the CHURCH has to decided weather or not the previous marriage was valid or not. I'm afraid I cannot tell you for sure if the marriage was valid or not. Weather or not the couple had children doesn't matter.
Anyway, it would be best for the person in this situation to pray and ask God if He wants him to be pursuing this woman at this time while obeying God by remaining chaste. Although this may be difficult, by following God's Will we will never be disappointed in the end. I really hoped this helped and if you have other questions feel free to ask them. Be assured of my prayers and God Bless!