Answer:
Yes they do.
David’s son by Bathsheba (even though conceived in sin and in an adulterous relationship) still went to heaven. It is clear by David’s statements after this young babies death.
2 Samuel 12:21-23 Then said his servants unto him, What thing is this that thou hast done? thou didst fast and weep for the child, while it was alive; but when the child was dead, thou didst rise and eat bread. And he said, While the child was yet alive, I fasted and wept: for I said, Who can tell whether GOD will be gracious to me, that the child may live? But now he is dead, wherefore should I fast? can I bring him back again? I shall go to him, but he shall not return to me.
We also know by what Jesus said, that the young children who were still innocent in their ways and did not know better where part of the Kingdom of Heaven…
Luke 18:16 But Jesus called them unto him, and said, Suffer little children to come unto me, and forbid them not: for of such is the kingdom of God.