Not sure if you've had your S&S yet, but just found your post!!
I had one with my DD one afternoon, the next morning I lost my plug and started having regular contractions. So IMO they definately work. Generally I think if you're body is part the way there, you will go into labour within 48 hours. But having said that, if your cervix isn't favourable (ie. still high and firm) it can be plain uncomfortable and unsucessful.
Being 39+4 I would say give it a go for sure smile I would line up for one again this time if I go over due! The only thing, it REALLY hurt me!! Apparently it's normally just uncomfortable like a pap smear, but I had tears in my eyes and had a really rough male OBs who wasn't very gentle. But usually it's just uncomfy and it's over in seconds.
Let us know how you go smile So excited for you!!!!