According to the Argonne National Laboratory's Ask a Scientist site, newborn babies are not able to breathe underwater. Immediately after birth, they are still connected to their mothers and receive oxygen through their umbilical cords.
Ask the Scientist points out that "breathing" means a gas exchange involving the lungs, so this definition precludes "breathing" underwater. Once the umbilical cord is cut, the baby must be allowed to breathe air.
South Carolina's Charleston Birth Place points out several factors that prevent babies from breathing underwater during a water birth. For example, at birth, the baby's level of the chemical "prostaglandin" is high, and this inhibits breathing muscles. In addition, Charleston Birth Place indicates that newborns have dense fluid in their lungs, and water is not able to displace it.