Can a neck injury stunt the growth of a fourteen year old?

No. Teen growth occurs from the long bones rather than the spine. The growth plates in the legs close on average starting at age 15 and ending at age 20. Unless the neck injury involves more than the bones in the neck, it should have no effect on when the other growth plates close. (certain medications used to treat injuries, may cause premature closure, though.).
No. A neck strain or injury which has not caused any paralysis will not stunt a child's growth.