The officer CAN issue a citation, PERIOD. The officer is an officer with full authority, 24/7. While most won't give out tickets, except for SERIOUS offenses when they are not officially on duty, they have the authority to do so.
In addition, many departments use unmarked cars for traffic enforcement.
That said, if the officer is not in uniform and not in a marked car, I suspect a jury would dismiss any additional charge for not pulling over anywhere other than the nearest police station or for calling 911 while continuing to drive to verify they were actually an officer.