I've thought about this question for a day. In all communication there is a sender and a receiver. If your son has the talent, desire and maturity to reach out to coaches then I don't think there is a specific age limitation. However, I don't think you can expect a reply from every coach you reach out to unless you tie it to someone the coach knows or trusts.
Put yourself in the coaches shoes, would you reply to the hundreds of emails, phone calls from high schoolers or their parents....probably not. Would you reach out or follow up with recommendations from travel coaches, Legion coaches, or high school coaches? Definetly a lot more likely IMHO. I know if I was in their position, I'd leverage the people I know and trust to tell me where the talent is or see the talent with my own eyes to verify.
So, to answer the question directly. Send the coach an introduction but tie it to a team or a coach he may know so there is at least a chance he'll follow up. Again, JMO.