Usually, the district assemblies start past the middle of June, but I have heard a number of people that have had them start already. Granted, that is in the South where school usually lets out in May and starts in August. On the flip side, some southern assemblies might be running in late August and school already in session.
I have seen a district assembly that ran June 16-18. And school didn't let out that year until June 23. This is the week when final exams are commonly given in school, and any children that missed them for the a$$embly got a zero on the biggest test of the year and likely flunked or did poorly as a result. No, that wasn't in the south either. It was in the North, where school still had another week. I bet the children who flunked the finals for that a$$embly got high praise in the magazines (and yet, they got prodded to do even more).
The circuit a$$emblies run the weekends and do not force the attendees to miss school. Special meetings, though, might. They might also have special meetings at the Kingdumb Hells that force children to miss school, and there is always service that cuts the last class short in some districts.