It's definitely not a good idea to mess with medication without the advice of your doctor. Your period is a healthy natural function--it helps flush the vagina clean of bacteria and prevents endometriosis.
Sometimes, it is possible for a doctor to advise you to skip your placebos, BUT that should only be done with a doctor's advice. For example, if you try to skip a period without a doctor's consent, you can build up an unusually large amount of lining in your uterus, which is no good.
In short, don't try to do it without a doctor's consent. We really don't know the long term effects of not having periods, but we do know that the normal menstrual cycle is healthy.