A sling bag you're going to have to put into a locker. Mac is being sweeter than me by saying to contact Guest Services, but I would say that the answer will be "no".
A waist pack is much smaller and is allowed on some of those rides.
I was at UO in the ugh ugh heat on the 24-27th, and once you moved your way to the back of the locker area it didn't take much time. Any time WE took was because we had TWO backpacks that were large, and we had to shove them in. And DS is down an arm (broke it early August) so we had to go one at a time. Then we were at USH in July and on the 1st of September, and again, no problems with the lockers (though USH Mummy locker area is a broiling hot disgusting MESS, and we ended up saying "whatever", though I think there was a swear involved and paid for a larger locker for a longer period of time b/c the free lockers at USH were the size of a pea LOL and had lines for what seemed to be ages).
If you have a non-rider holding your bags, be prepared to tell them that allllll throughout the queue!