A.H.
I did Little Gym with my oldest when he was about that age. He is also very active, and very athletic. We did 2 or 3 rounds of it I think. He had a lot of fun, but he did have issues with waiting his turn and standing in line (prior to doing an activity like the beam, bars, or somersaults or something).
They mostly just let him do what he wanted within reason of course. He isn't the type to intentionally hurt anyone, so if he cut in line, they would just gently tell him to move back, and he was usually okay with it - sometimes he's stomp his feet in frustration or something. He also would get under the parachute (those giant colorful parachute things), when he was supposed to be holding it or otherwise. They would constantly have to tell him to get out or whatever. He often didn't want to do the organized event that was happening at the time, and would instead run around and climb on the equipment elsewhere.
Come to find out (just a few weeks ago actually, and he's 7 now), he has a language/listening disorder... Explains a lot...
But anyhoo, you could certainly give it a try. Probably wouldn't hurt anything.