As has been mentioned by a few others, the autism spectrum is very broad and different kids will have different tolerances.
I have flown for an organization called Challenge Air for Kids and Friends for about five years. They hold an annual event at Fort Lauderdale Executive Airport which is designed to give short airplane flights to disabled kids. During those events, there are kids with all kinds of disabilities, but the majority seem to be autistic or have a form of Palsy. As such, I have flown many kids, some of which are extremely disabled and some of which are extremely high-functioning.
I have had all kinds of different experiences flying those kids. Some react very well and have a wonderful time. Other children do not react well to being in the airplane, the noise or the motion. In my case, a parent or guardian is always in the airplane.
My usual process is to evaluate the child on the way to the airplane and assess the level of the disability. I speak with the parents about what the child is going to experience and find out what kind of reaction to expect. In a normal situation, the child would ride up front with me, but if I have concerns, the child rides in the back with the parents. When we get to the plane, I do a complete briefing, but in most cases it is for the parent, not the child.
If the child is in the front seat with me, I allow them to fly the airplane once we are airborne. However, I also brief them to keep their hands on their laps and off the controls when I say so. The ability of the child to comply depends upon where they are on the spectrum.
In the times that I have done these flights, I have had numerous wonderful experiences and a few that were memorable for other reasons. However, I plan on continuing to fly these events and would highly recommend the experience of introducing an autistic child to the thrill of flying an airplane.
Abram