Doesn't sound like ADHD to me, so no, I personally wouldn't encourage any testing in that area - ADHD is meant to be a diagnosis of last resort, but is all too often diagnosed without looking into any other possibilities. I would say go for private testing with a psychologist who can also do a test like the Woodcock Johnson or the WISC.
What are the consequences he faces when he behaves that way at school? Regardless of his IQ score or ADHD, he needs to have consistent consequences for inappropriate behavior.
