I did it about 12 years ago in mid july, it was a low water year and it was low in places. We had to drag around a few log jams on the main river but it was fine. We put in way up on Youngs creek and that was LOW with a lot of dragging, cursing and awesome fishing. The float window will depend on when, what kind of water year it is and your tolerance for pain. There is no white water, I guess there could be early season but I don't think your going to get in there during true high water - the trails will be impassable. When the snow is gone and you can get in, the water will have been on the drop for a while. The big concern at higher flows would be log jams - coming around the corner and finding river wide jams was common when we went. There was usually a route through but it took some scouting occasionally. Typically the log jams occur in areas that get really braided and the river is really wide and shallow - so usually very slow. You get out and walk the boat around to find a path.
Awesome trip but the fishing is way better away from commonly used camping areas. When I do it again I'll be spending the majority of my time on Youngs creek and at the confluence. Then I'll haul out through the wilderness highway in a couple 3 days. It gets really crowded in there in mid July! We saw a handfull of people the first 3 days, then were rarely out of site of people after that. We were in there 8 days I believe including the hike in on the first day and a half. It took 2 days to get to the confluence from where we started floating (the confluence of Youngs creek and Babcock creek). There is a narrows on Youngs creek that was very shallow for us, but with another foot of water would have been some fun, but easy white water.
"If you dont do it this year, you will be one year older when you do"