To be successful in our world you have to learn to inhibit impulses and use language. Inattention and distractibility are not a problem if kids are interested and invested in a task. As these things become less, the ADHD kid will have less problems. ADD without hyperactivity is a whole separate problem - a disorder of vigilance. ADD kids get in trouble for showing emotions.
Contingency based rewards become rule governed after a time.
They don't catch the cues in the same way as non-ADHD kids. Incompetence is not non-compliance. ADHD is a disorder of inconsistency. It is not a time limited disorder. It is not determined by a single gene, but part of a very complicated system where protective genes may play a part.