Don't most hormone based birth controls use placebo doses and still have effective rates of like 98%+? This doubly applies here, because most women are fully aware of which doses are the placebos.

I have always understood the placebo effect as the belief that it makes you feel better, not an actual effect that makes you better. However believing that it makes you better, leads to lower stress, which leads to lower inflammation, which does lead many people to feel better to some degree. Anti-inflammatory tactics are exceedingly common treatment for various conditions. You may call that superficial, and only an imitation of a treatment, but… that is what the placebo effect is also all about.