Yes, however, the case would be more difficult.  So they created a rule/law where in order for the PIP to pay the medical bills of a car accident, you must be seen at the hospital or at a doctor office (and presumptively complain about injuries from the accident) within 14 days.   If you don’t go, then your medical bills would not get paid but would be part of your claim against the wrongdoer.  However, if you did not go to see a doctor until 15 days (for example) it would beg the question of why you did not go to the doctor sooner.