Will a fractured skull in a baby cause brain damage later in life?

Depends: How did the fracture occur? Was there a fall? If the brain sustained a significant deceleration injury there could be damage to the nerve fibers of the brain. Some areas of the skull are thin and more easily fractured so less force would be transferred to the brain. More force could cause concussion, contusion, bleeding, and yes, a permanent injury.

Maybe: The fracture itself can occur with little long term effect or a lot, depending on the injury at the time to brain tissue. Babies, different from adults, have a greater capability of rewiring past problem areas, so a long term recovery is more likely for babies. Overall, it depends on how bad the initial brain injury was in the beginning.