Darlene and David never had a child; rather, Darlene and Mark had a child. Although the baby nearly died, it did survive.
Darlene was never even with David, and Becky was never with Mark; it was the other way around.
This is all explained at the end of the series finale, "Into the Good Night (Part 2)".
"When Becky brought David home a few years ago, I thought, 'This is wrong; he's much more Darlene's type.' ... When Darlene met Mark, I thought he went better with Becky. ... I guess I was wrong. But, I still think they'd be more compatible the other way around; so, in my writing, I did what any good mother would do: I fixed it.
And then Darlene had the baby, and it almost died..."
--Roseanne, Season 9, Episode 24, "Into the Good Night (Part 2)"
Actually Darlene and David were a couple. Mark is David's older brother and married to Becky, Darlene's older sister. Darlene and David got married because she was pregnant and then the baby almost died, but to answer the question...yes the baby survived. (This was retconned in the final episode of Roseanne, 'Into that Good Night'. Roseanne was writing a book based on her life and changed some stuff around. Because she thought David was Darlene's type rather than Mark, in the book she made it that David and Darlene were a couple who had a baby together. Darlene and Mark were actually a couple and it's assumed the baby that almost died was Mark's. This is all mentioned in the comment above.)
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