V.,
I did not have this done, but a friend that I work with did. She was 39.5 weeks and only 1 cm dilated, if that. No signs of labor starting any day. They did it, but it did not work. Almost 2 weeks later she had to still be induced with pitocin and something else. She gave birth to an over 9 pound baby.
In my case, I went back for a drs appointment the day before my due date. I was already 3 cm and just simply by her checking me, she accidently tore a hole and my water started leaking. I had to be sent to the hospital so they could start inducing me to bring on contractions.
I guess the thing is, if your body is showing signs of being "ready", the measures they take will work. If it's not ready, nothing short of them hooking you up to an IV is gonna effectively start labor. Hang in there, you are almost done! COngrats on the new baby.