Homeopathic "remedies", like herbal "remedies"* are classified in the US as dietary supplements. As such, they are subject to very few regulations, but they are required to list ingredients. So, if you want to down a whole bottle of homeopathic pills to demonstrate their lack of effect, you can check the label to make sure there's no other crap in there that might have unpleasant side effects. (And this is an excellent idea, because many of them do contain other crap.)
Unfortunately, the guys who make these pills don't seem to be very careful about labeling the actual ingredients. There have been several cases recently where both herbal and homeopathic remedies have been found to contain things--often significant active ingredients--that aren't on the label. And yes, I believe there have been unfortunate side-effects. So I'd hesitate to try the trick without getting some independent verification of what the label says.
* In fact, I suspect that most US consumers of homeopathy have no idea what the term means, and think it's some specialized type of herbal or "natural" remedy.