This article is from the ER FAQ, by Rose Cooper email@example.com with numerous contributions by others.
Yes. Though the writers seem to have forgotten it. Thank goodness.
Only two episodes mention it, however. In "Hit and Run" , Doug
is asked by a patient`s father if he has any children, and he says that he
has a son. In "Luck of the Draw" , he`s asked the same thing by a
patient, and replies, "I have a son; he`s eight." Having overheard this,
Nurse Wendy Goldman later says, "I didn`t know you had a son. What`s his
name?" Doug says, "I don`t know, Wendy, I`ve never seen him."
The conventional wisdom is that this son is the result of a
liaison Doug once had with a woman he no longer keeps in touch with,
and that the child was very likely born after Doug and the woman had
severed ties. One theory is that Doug left this woman after finding
out she was pregnant, because he couldn`t bear the responsibility of
fathering a child. [My personal favorite theory is that Doug was a circus
worker who, upon being stomped upside the head by an elephant with Issues,
Got Amnesia and...uh, wait, that's my favorite "Days Of All My Young And
Beautiful Children" theory. Never mind...]