I have experience of this from a different point of view, if it helps.
I suffer from chronic back and pelvic pain, but can't have my usual trigger point and nerve block injections as I am pregnant. My pain management consultant recommended that I try acupuncture instead. However, she said there have been studies done that supposedly show that acupuncture brings on labour, so it is not recommended in pregnant women - the hospital's acupuncture practitioners will not go against guidelines, so the consultant herself is doing my acupuncture.
She said that in her medical opinion, acupuncture in the last few weeks of pregnancy doesn't bring on labour, it's just that the likelihood of you going into labour is v high at that time anyway.
She also said that in her opinion and experience, in cases where ladies have been receiving acupuncture while pregnant but not yet full term, it's not the acupuncture that brings on labour, but the extreme amount of pain that they are in that has forced them to try the acupuncture in the first place.
As far as acupuncture being "woo" goes, perhaps it is when it comes to things like bringing on labour. But it is truly helping with my back pain. Fair enough, it's not touching the grinding bone/disc pain, but it's definitely helping with my muscle spasms.
So I guess if it's money you can do without, then where's the harm in trying, really? It might bring labour on, or labour may have always going to have started at that point, there's just no knowing.
FWIW, I don't think it hurts at all. It's a v different sensation to what I thought it would be like. Not sharp, but more a pressure, like someone pushing hard with their thumb. It's v relaxing too, I tend to have a nap while the needles are in!