Do neonatologist perform surgical procedures on babies?

NO. They can place catheters in the umbilical artery or vein. They can intubate your child. They can perform lumbar punctures. However, they cannot do surgical procedures.
Define surgery. Some of the common procedures done by neonatologists (catheter placement) are considered surgery by the insurance companies. We don't consider them as such, but the bean counters have a way of controlling how things are classified. Neonatologists are not going to fix hernias or take out an appendix.