I don't think they are meant to bring on labor but they can help ripen cervix in late pregnancy. When I was in early labor with ds#1 I wasn't comfy and had a lot of pressure down there. I did squats to help stretch and alleviate the pressure and it did seem to help thin cervix. It also helped me stay active and take pressure off my back. The motion is similar to bouncing on a ball so I don't think it could hurt.
I do some squats every day as part of my normal workout. They help stretch and strengthen leg and hip muscles that could help in labor. deep squats I think are what you are thinking about trying to bring on labor. I still don't think it would bring on labor but if your doc is ok with it, then it is worth a try (after 37 weeks)
as always, double check with doc to be sure your body and lo can handle it. Best of luck.