I'm heading down in a week (Yaaaahooooo) for my ninth straight second-week of June visit. The crowds are noticable, but aren't obnoxious by any means. If you use "commando techniques," such as early mornings, heavy fast pass usage, etc, and are willing to simply walk away from a line or two (I've never ridden SM in June), you won't wait more than 15 to 20 minutes.
Gay Days are going on that week, which has an affect, mostly on PI and MK on Saturday night the 7th. There's always a lighter crowd the first week of June than the 2nd, but we're expecting the lighter crowd effect to continue a little, due to so many school districts going later into June here in the northeast.
All-in-all, I'd rather go in September, but it's mighty managable. Note, when people asks me what sticks out about June, the crowd's aren't what comes to mind first. It's the heat. Three solutions: drink water, drink water, and drink water.
Pat