Only if they catch it when they are older, like in their teen years and beyond. Since the chickenpox vaccine wears off, it actually increases the likelihood that someone will catch chickenpox when they are older and more susceptible to permanent damage while if they leave it alone, a young child with chicken pox has permanent immunity and no permanent damage to their reproductive organs.
Sorry, we must have typed at the same time. But another fact: Infants are not a risk group for Hep B, but that is the first vaccine given at birth. If a person gets Hep B and fully recovers, which is very likely, that person will be immune the rest of his or her life.