Did Adam and Eve have to have kids?
God issued a command to all of the rest of His creation on Earth to be fruitful and multiply.
He provided Eve to Adam to help him to fulfill that role, among other things. Clearly, God made it clear that Eve would bear children because some of the comments God made after they sinned concerned offspring (Gen. 3:16). The name Eve, itself, means mother of all living (Gen. 3:20).
So all in all, I'd have to say that kids were required and would have been a result in their lives regardless of whether or not they had sinned and fallen out of God's grace. Of course, their lives would have been a whole lot better if they had stayed in God's will, but there's nothing to be done about that now except making sure that we get right with God.