This has actually been researched and the science is pretty clear on this one: the placebo effect is very real and does work. As a matter of fact IIRC (sorry, c

This has actually been researched and the science is pretty clear on this one: the placebo effect is very real and does work. As a matter of fact IIRC (sorry, can't find the paper) some experiments with the principle as you describe have been done and came to that same conclusion.