Could a posterior cruciate ligament (pcl) heal itself over time?

Usually not: Pcl injuries, if complete, have zero healing potential. In partial injuries (sprains) depending on your age and other factors healing is possible.

Yes: The majority of people with PCL tears do not have surgery. There are three grades of PCL tears 1, 2, 3. The general rule is that surgery can improve your grade by one notch. Thus if you are a grade 1 or 2, then surgery probably not needed. If you are not super active and do not have symptoms then surgery not needed. Good rehab focusing on quad strength will go a long way in this injury.