UK Apologetics Reply:
The short answer is No. The official answer of the Roman Catholic Church to this all-important question was actually recently revised in 2007, when the International Theological Commission released a ground-breaking report, and Pope Benedict XVI approved it's findings.
In 2007, after extensive theological research, the commission has reported that there is a possibility that these unbaptized babies can go to heaven. They do agree with past findings that there is no definite answer to this question in religious documents, however, the commission has found that there is enough evidence to revise the official Roman Catholic Church opinion.
Traditionally, the Roman Catholic Church has always taught that the unbaptized baby's soul goes into a state of limbo. In this state, the baby's soul enjoys happiness and contentment for eternity, yet lacks the perfect joy of being with God. So the child's soul was seen as excluded from Heaven, yet not suffering the ravages of Hell or Purgatory.
That stance has now changed. In a report by the Associated Press, Rev. Luis Ladaria, the secretary general of the International Theological Commission, is quoted as saying, "We can say we have many reasons to hope that there is salvation for these babies." (http://news.yahoo.com/s/ap/20070420/ap_on_re_eu/vatican_limbo).
This new stance of the Church means that perhaps these babies do go to heaven, although, "perhaps" is the important word to note. The Church is not saying that they positively go to heaven, but that there is a possibility that they do enjoy eternal salvation after all. Yet - contrary to popular opinion among certain Protestants - the Roman Catholic Church has never taught that these babies souls are "damned."
Of course, the Roman Catholic Church still highly recommends that all babies be baptized so that they will (in the church's opinion) surely go to heaven.
The International Theological Commission was urged to do extensive research on this question because of the ever growing number of babies who die without the chance to be baptized. Due to the high incidence of abortion, in addition to baby deaths due to disease and war, it has become more urgent for the Church to research and clarify their official opinion on this matter.
Robin A. Brace. February 10th 2010.