This discussion might more properly belong in the Lore and Roleplay area.
I don't think the officially-released lore discusses the children of slaves. Obviously, the children of regular slaves are slaves too, just like with historic slavery on Earth. But I do not know if this extends to Imperial Slavery. Nominally, Imperial Slaves are still citizens, who have (temporarily) renounced their rights as citizens in order to pay off a debt. If two Imperial Slaves, or an Imperial Slave and a Free Citizen, have a child, it seems to me to stand to reason that the child would on paper be a free citizen too. However, if the debt is large enough, it seems likely that one person;s life work could not cover it, so the debtor's entire family, including non-adult children, might be sold into slavery too. The Empire has enslaved entire planets in the past on this basis, and I can't see them giving exemptions to children.
Of course, it's also entirely possible that, as part of the process of becoming an Imperial Slave, their capacity to have children is also surgically, medically or genetically removed from them, which would largely remove the basis for the question.