I would want to know what he's being evaluated FOR, honestly. And it sounds very vague at this point. Again, why a psychiatrist vs a psychologist? Definitely ask a lot of questions and meet the evaluator before you agree.
Also, I agree that a trial period in the older classroom would provide some insight as to whether his behavior will change in the new setting. You mentioned an after-school science class that he does fine in. Are the other kids in that class older than him or more mature than those he is around at school? If so, it might be a good example of what he might be like in a different setting.
As for the older kids being less forgiving, this could be a good thing, IF the behavior is not a consequence of a 2E factor that he can't control. If he is just acting out from boredom, then a more stimulating environment plus more mature classmates should solve the problem. If you suspect 2E issues, though, I don't know that I would trust this evaluation from a school chosen psychiatrist. I would probably prefer a neuropsych eval from a doctor of MY choosing.
