Someone can definitely be gifted and have ADHD. I think most teachers in the public school system are quick to find something wrong with kids who don't thrive in the "normal" school setting. If you have the financial means, I would get an official evaluation from a private evaluator (not one from the school). They can run a more extensive battery of tests which include and IQ test as well as various testing for ADHD symptoms and behaviors. This would give you a good idea of where your child's strengths and weaknesses lie and if he is in fact just bored or if there is something else going on. Or a combination of both.