Could exuberant knee reflex be a symptom of spinal cord injury?

Yes: Nerves originating from the brain suppress reflexes to a degree. With certain spinal cord injuries, this suppressive effect is interrupted, and reflexes can be very brisk as a result.

Yes but it would : Need to be correlated with history of patient and other exam findings as well as imaging studies. A brisk reflex can be normal or may be found with certain spinal cord or other neural pathologies.