So I did more research on this and found that there are thoeries trom theologians suggesting that they might go to limbo because they have not commited sins themselves.
But the answer is that yes they would be excluded from the beatific vision a baptized baby would get. Whether they go to the unproven limbo or heaven I can’t know.
1257 … The Church does not know of any means other than Baptism that assures entry into eternal beatitude; this is why she takes care not to neglect the mission she has received from the Lord to see that all who can be baptized are “reborn of water and the Spirit.” God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments.
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1261 As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus’ tenderness toward children which caused him to say: "Let the children come to me, do not hinder them,"63 allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church’s call not to prevent little children coming to Christ through the gift of holy Baptism.
I believe it was St John Paul II who commissioned the International Theological Commission to study the question of infants who die without being baptized and the above link is the result of their inquiry.
As you state, the magisterium of the Church has said “Souls who depart this life in the state of original sin are excluded from the Beatific Vision of God.” One poster has noted from the CCC, however, that “God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments.” Accordingly, it is possible that God in his mercy removes original sin from infants who die without the sacrament of baptism, possibly by the desire of the Church for such souls - baptism of desire, and thus these infants go to heaven and are not excluded from the beatific vision. As the document from the International Theological Commission says as well as the CCC, the Church does not know with certainty the fate of such infants who die without baptism; God has not revealed this but the Church entrusts these souls to the mercy of God. Yes, the Church has said that “Souls who depart this life in the state of original sin are excluded from the Beatific Vision of God.” However, the Church also believes that “God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments.” So, maybe, these infants do not depart this life in the state of original sin but God out of his mercy himself removes the stain of original sin from the souls of these infants before death. As the Church says, this hope in the mercy of God for such souls does not diminish the necessity of baptism in the ordinary course of events as Jesus himself declares for entrance to the eternal kingdom of God. Infants who die without being baptized are a special case of which the Church does not have any certain knowledge of their eternal destiny; although the magisterium has said at least that they do not suffer the eternal punishments of hell as a person who goes there because of unrepentant personal mortal sins.
Limbo is speculated on where unbaptized babies go. It would be a part of hell (not of the damned) just how purgatory is a part of hell. They will be in Heaven after the Final judgement. So yes, they do go to heaven but not immediately. St. Augustine taught that they went to the hell of the damned which makes no sense. I hope that answers you question
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