He is most likely bored. No, the school should not remove him from the program due to ADD/ADHD. If they try, you should research Section 504. You can request a conference and set up an IEP (individual educational plan) with the general education teachers. Your best line of defense is a good offense. Make sure you know the laws and rules of your state and the school he attends. Be a advocate for your child. Goodluck.
Maybe he is bored - my son has been in a gifted and accelerated school since pre-k, he is in 2nd grade now. I do not believe they would make you remove him from the school IF he were ADD or ADHD, he's there because of his IQ. Make sure you find out everything that's going on at school, maybe he's having problems with another child. There are alot of challenges in raising gifted kids, but there are alot of resources out there to help. try googling "gifted associations". Hope i helped.