Yes, but you have to BELIEVE the placebos will help. In fact, the paradox ONLY appears in the case you know it's a placebo because that's when the feedback loop can happen.
I'm not aware of any research that says a placebo won't help a "non-believer" - can you cite a study? Given the study I linked where they were deliberately handed inert pills and told that they were an inert placebo, and they still worked, I actually strongly doubt your claim.
And given the research I linked, why in the world wouldn't you believe in them? They do rationally work.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
If continuing the discussion becomes impractical, that means you win at open threads; a celebratory top-level post on the topic is traditional.