He will be treated the same as any other foreigners. Nothing more, nothing less. The special treatment visa category won’t apply to your son as you already stated. Your son won’t be disadvantaged over other Americans entering or working in Korea.
My son also did the same thing years ago. He couldn’t possibly serve in Korean military due to language and cultural issues. Although he has great appreciation for Korean culture and heritage, there is no chance he will work or live in Korea. I don’t think he will visit Korea on his own unless we live there, which we don’t plan to.