My 9-yr old son is ADHD, he thrives in a structured setting. Currently he's attending the Franklin West campus. He still has a couple days during the year where his gregariousness gets him into trouble, but he does know that it's not appropriate for him to chat with everyone during class. Surprisingly, he's not bored in class, which was often his complaint at his other school. Previously, he was attending a charter school that had more group and exploratory learning. His grades were fine, but the loose structure meant that he competed with the teacher for talk time, which led to much the same problem that your son seems to be facing. Many times, he'd be the first to finish the activity, would help his group finish early and then they'd do whatever they wanted. Currently, his teacher has them pull out a book to read or some quiet activity that they can do while the other's finish. (Franklin students have their own desk, they sit in neat rows and columns.)
I would say that it's worth the troubles to send your son to a more structured school. I'm not advocating Franklin schools for all children or that style of instruction, but it really works for my 9 yr-old. When my 3 yr-old starts school, I'll see what works best for him.