Will I ever completely heal from my C2 spine fracture?

Yes you could if . Properly treated. Complications of c2 fracture treatment are nonunion, malunion, pseudoarthrosis formation, infection, neurovascular injury, acute airway compromise, and hardware failure. The risks of nonunion, malunion, and pseudoarthrosis formation are lessened with surgical treatment. As with any surgical procedure, risk of infection always exists.
Hangman or Odontoid. Depends where your fracture is located. Odontoid fractures are divided into 3 types. Only the type 2 is likely to give much trouble as they fail to heal as much as 50% of the time. The hangman types involve the ring of bone. Low likelihood of nerve damage, and most heal uneventfully unless fracture is through the joint or displaced. Generally speaking, yes to your question. But could take 6-12 mos.