Behavior problems can certainly be the result of frustrations at school. Especially if a child feels like no one understands (or cares) what's wrong, he can act out in wildly inappropriate ways.
I don't know that this is what's happening in your case. I think you need more evidence. Lots of things can cause angry outbursts. But GT anger and frustration is one possibility.
When my always-before pleasant child became nasty and angry at age 6, it was clearly tied to school. He told us as much and there really wasn't any question about it. But it is certainly possible for bad behavior to spill over into home life if a child is unhappy at school (or vice versa).
I think it's also worth remembering that different kids are differently self-aware about what's bothering them. My son is and always has been very self-aware, so it made sense that he knew precisely what was triggering his bad feelings. But certainly not all kids--even GT ones!--would be able to ID it. They might just know that they feel bad. Especially if your DS thinks he shouldn't be unhappy at school, he might not tell you that's what's bothering him.
I guess I'm saying that I think you need more information if you're going to figure this out. I don't think you know enough to tell whether his behavior is related to school or not.
Can you observe him at school? That might help.
You might also ask him to pay close attention to his feelings one day and pinpoint for you what is happening each time he feels angry or upset. If he's capable of doing that for you, it might draw you a pretty good picture of what's wrong. Would the teacher cooperate with you on this by letting him write a few words/draw a quick picture every time he gets upset so that you have some record of what his emotional day was like?
You might also try asking him what were the best and worst parts of his day. That might tell you as much as you need to know.
It's so hard! Best wishes to you!
