It will be slammed, but the main things that will be affected are the big rides. If your kids are only interested in the smaller rides, it might not be terrible. The park will still be difficult to get in and out of, and around in.
Honestly, for your first visit I'd skip Saturday. YCW is a circus and not necessarily the best time to experience the city unless you like dealing with thousands of young teenagers and whatever is hip in the christian music scene these days.