Can a physically healthy, married couple honor God without having children? If a married couple is physically able to have children (at least potentially) can they honor God without having children?

Roman Catholics, for example, say that sex has at least two purposes according to God: uniting a couple and producing offspring. Therefore if a couple is able to have kids they should at least try to at some point in time.

Under what circumstances would other church doctrines weigh in on whether or not a couple, otherwise able to have children, might choose to adopt rather than procreate in the natural fashion?
Short Answer: Yes. Just as a person can honor God without getting married, a couple can honor God without having children.

From a Biblical perspective, Paul's advice in 1 Corinthians 7:17-35 is highly relevant:


  Only, as the Lord has assigned to each one, as God has called each, in this manner let him walk. . . . Was any man called when he was already circumcised? He is not to become uncircumcised. Has anyone been called in uncircumcision? He is not to be circumcised. . . . Each man must remain in that condition in which he was called. . . . Brethren, each one is to remain with God in that condition in which he was called. . . . 
  I think then that this is good in view of the present distress, that it is good for a man to remain as he is. Are you bound to a wife? Do not seek to be released. Are you released from a wife? Do not seek a wife. But if you marry, you have not sinned . . . . Yet such will have trouble in this life, and I am trying to spare you. But this I say, brethren, the time has been shortened, so that from now on those who have wives should be as though they had none . . . and those who use the world, as though they did not make full use of it; for the form of this world is passing away. 
  But I want you to be free from concern. One who is unmarried is concerned about the things of the Lord, how he may please the Lord; but one who is married is concerned about the things of the world, how he may please his wife, and his interests are divided. . . . This I say for your own benefit; not to put a restraint upon you, but to promote what is appropriate and to secure undistracted devotion to the Lord.


Here we see Paul encouraging the saints in Corinth to stop worrying about trying to fit some external form and just serve the Lord. He lists off a whole series of questions where a person might be inclined to think that they need to "do" something different in order to please the Lord, and Paul's response is two-fold:


"I want you to be free from concern." The form of this world is passing away, so don't worry about it -- just remain as you are and serve the Lord
We are not talking about matters of "sin" here, so if you choose not to "remain as you are" (or, of course, if God leads you in another direction) that's OK too.


The reason this is a great passage to use in addressing your question is that God also created marriage for a specific purpose, which the Catholic teachings would also affirm. However, God created this before man fell into sin, and in the fallen world we live in, Paul suggests that his readers remember that this world is passing away, and so at the end of the day all that matters is devotion to the Lord.