I don't know. But placebos can have some pretty strange properties: if a doctor says a placebo is "extra strength", the patient will do better, if the pill looks colorful and complicated the patient will do better, if it's delivered via IV instead of pill the patient will do better, if the doctor wears gloves when handling the placebo because it's "so strong I can't even risk skin contact" the patient will do better, et cetera.

So there's no guarantee something flaky-sounding like "diet and exercise" would be as strong a placebo as a big name like Prozac, even if Prozac did work mostly by placebo effect, which, again, is far from certain. Try the drugs.