Does exercising/training at a young age stunt your growth for life?

No. This is a common myth but there is no evidence that moderate exercise will stunt growth. Inadequate nutritional intake or overtraining can effect growth, but exercise is recommended for all ages. Children are encouraged to get 60 minutes of physical activity daily.
No if done right. If done right and in moderation, there is no study that show any bad effect from exercise when you are young.