Answer from Bethany, SPHR, SHRM-SCP:
It would, yes. The birth of a child is a HIPAA special enrollment right, meaning the employee, their spouse, and their newborn child may enroll into the medical plan midyear.
However, it’s a somewhat common misconception to assume the employee can also enroll their other children, if they have any, at the same time. While it might be possible, depending on the provisions of your plan, we recommend checking your plan materials to be certain. Documents to double check include your cafeteria plan, if you have one, and your medical summary plan description.