As I understand it, you were either validly married on the day or not. If not, you are no more married than an unmarried person. The tribunal looks at the circuмstances and behavior in your marriage to determine the likely state of mind up to and on the day of your wedding. They cannot ever know for certain they just work on the balance of probabilites like any legal judgement.
A man could have a child or many children with a live in girlfriend of 10 years and be free to marry if he leaves her. A woman could have illegitemate children from many different men and be free to marry.
A priest who had abandonned his vocation could have a wedding have 7 children and would not be married. That is the nature of the sacramental bond. It either exists or it does not.
The marriage is determined to have never been real in the first place. Therefore pragmatic considerations such as the welfare of children should not be part of that decisioning process or if they are, ONLY, in the sense that they give evidence to the state of mind up to and on the wedding day.
This is why it is ridiculous for Mel Gibson or Bud MacFarlane Jr to apply for or consider an annulment. Because their married life suggests they were completely married.
Someone in a sexless marriage, however, suggests they (one or both) have no clue what marriage is about, its PRIMARY purpose. One child being born because his wife agreed to sex for one night, and then went back to refusing sex would demonstrate a completely perverted understanding of the duties of marriage.