Oops. My post disappeared.
I'm hoping I can help explain what's happening in his head.
I have ADHD.
I was reasonably contained at school, I was 'the nutty one' but I didn't misbehave as such.
Once I got to college, my behaviour changed entirely.
I honestly felt embarrassed of myself for it, I've always embarrassed easily. But I would pipe up, wander off, be inappropriate, I was a dick.
I didn't want to be a dick. It was like something inside me compelled me to behave like a dick.
Don't get me wrong, I've been a TA and kids who behave like yours are awful to be around (sorry). But he genuinely can't help it.
Some people with ADHD are more likely to act out, others less so. With me being female, mine got progressively worse after I left school. Boys tend to improve.
I think you and the school are right. It's a reason, not an excuse. But I also think your son needs some extra support outside of lessons to learn to have more control over his outbursts. I control mine much better now. My eldest is waiting for assessment but is being treated as if she has it definitely, by her school. They've asked her what helps, they've asked me my opinions. She needs to fiddle or doodle, while she's listening, so she doesn't done out or do something inappropriate.
Have a search on Amazon for 'fiddle toy', 'stimulation toy' etc. I got an amazing one from Asia which is plastic peas in a rubber pod. Took a while to arrive. But it feels amazing. It can be attached to a phone or keys.