If you believe the medicine is going to work it might. If you don't, it probably won't. That's the basis for setting up double-blind trials - but since they would normally the people invooved not being at all confident that it is going to work, you'd expect to get reduced effects either way.

Do they do double-double-blind experiments? That would be where the results included some from people getting placebos, where they (and the administrators) believed it was the real stuff, and others where it was the real stuff, but everyone thought it wasn't? Though no doubt that would be unethical.