When you have your child tested, that tells you a lot about your child. This is useful data for you and your child. However there's the risk that a parent might try to apply the information to situations where it really doesn't apply.
I speak from personal experience here. When we had DD tested, we thought that the information would a) give us predictive data about school and b) mean something of use to the school. Neither was true.
I believe that the success of a young HG+ child during a particular year of school is based primarily on the specific teacher. If the teacher "gets" your DS, it will be OK. If the teacher doesn't, its a lot less likely to work. Now the type of teachers you get at a school depends on the school culture and administration, but there's tons of variation. Which is why, as ConnectingDots indicated, Montessori works great for some and not for others.
Right now, your DS is giving you more valuable data than the test. He's telling you that he's bored and going crazy and that's what you need to listen to.
* I say young here, because once you get into the world of different classes / different teachers (usually in middle school) the issue is less acute. A child might have one teacher a year who gets him or her and that can be enough to get them through the classes with the teachers who don't. But for a little kid, that teacher is a huge part of their world and had a huge effect on their self concept as a student.