My eldest daughter started gymnastics at 3. My youngest started at 15 months.
With DD2, At the beginning, I would say she was a little young - there was a lot of stuff she couldn't really do, but by 18 months, she could pretty much do anything like the rest of the children. However, I went for the social side (never got on with playgroups - found them to be an awful experience), but through the gymnastics classes, I made friends and am still friends with some of the mums several years later. I also took her because her elder sister went and she kept trying to join in.
At our gym, the under 3s were in a class with their parents. At 3, you had the choice of staying with them, or letting the children do the class alone. DD2 did the class then with her friends. I would say that it was excellent preparation for school, because in that class, the children would be taken over to a circuit, they'd sit and watch the teacher complete the circuit (about a minute or two) and explain what they'd have to do, and then they'd complete the circuit themselves. It was fantastic in terms of listening skills, concentrating, following instructions etc, everything they need to develop for school 
.
I would say that starting young, DD never had any fear of the equipment. She's grown up around it, and so has never worried, whereas children coming in later have had more fear of the beam, the height etc.
I originally wanted some kind of tumble tots class (just something to burn my daughter's energy off), but quickly noted that tumble tots was just a franchise, so the owner did not necessarily have any specialist training, whereas at the gym, they did pretty much the same thing, but instead, they had proper gymnastics equipment, with sprung floors and soft play, and a specialist preschool coach, who was paediatric first trained, and was actually cheaper than the tumble tots class that didn't offer any of this!
Certainly, in my daughters class, it was all based around age appropriate fun. The warm up was a game and a song, the circuit included a children's slide to play on, jumping in the foam pit at the end was always the highlight. To put my teacher's hat on for a second, I would say that it worked widely within each child's zone of proximal development, so each child developed skills, and grew in confidence. Certainly, my children loved their classes and their coaches.
I can't speak for other gyms, as I do not know how they organise their preschool classes, but I wouldn't hesitate to recommend my daughter's gym. Both my girls got a lot out of them, and they both still love gymnastics to this day.