In regards to crowds, the answer is a definitive yes, August is generally the busiest time of year. It's a permitted route and there is a lottery. You must camp at designated campsites. The lottery happens in late winter/early spring. If you can be flexible with start/end dates that works best. Even without a permit, they do keep some available for walk-up, but then the choices for campsites can be limited.
All that said, it is far easier to get a permit in September as fewer people want a permit then. It still books up but tends to be more flexible. I personally would go for late August/early September. There tends to be fewer bugs later in the season, much like Montana.
I am not a trail runner but have hiked the Wonderland and section hiked it many times as it's close by....I would consider the west side to be the toughest (and less crowded) section because it has greatest gain/loss...You start at Longmire and follow the trail clockwise. It's an easy to access start point. The advantage of starting at this point is that you can even stay a night prior to your hike camping or in a park lodge or alternatively, just outside the park at one of many hotel/b&b places.
You could do something like -
Day 1 Longmire to South Mowich River ~30 miles
Day 2 South Mowich River to FryingPan Creek Trailhead ~32 miles
Day 3 FryingPan Creek Trailhead to Lonmire ~31 miles
Another tough Day 1 would be:
Day 1 Mowich Lake to Summerland ~ 32 miles
Day 2 Summerland to Pyramid Creek ~ 31 miles
Day 2 Pyramid Creek to Mowich Lake ~ 30 miles
These aren't the camp spots everyone wants to stay at - but if you are running all day and great camp sites aren't the reason for going,they will do the job just fine.
There are many day hikers on certain sections of the Wonderland on weekend. Thus, I'd advise you to avoid the weekend if possible, especially in areas that draw greater crowds, such as the stretches between White River and Summerland/Indian Bar as well as selected areas near Mowich Lake (especially if you elect to go Spray Park instead of the official Wonderland route, which is less scenic) and some congestion near Sunrise.