Every study I've seen on this (good and bad) has said that people who take the HCG (HHCG or good ole fashion injections) experience similar weight loss to those taking a placebo. If you follow this protocol with or without drops, you are GOING to lose weight. It's simple math of calories in vs. calories out. That said, the thing that peeked my interest was that in one study the HCG takers had no muscle loss. Of course this could be due to the high protein - low carb thing. I don't know. I'm on my second round of HHCG, and I am losing weight at a rate of about .5lb a day. Respectable, but I'm almost thinking I'd rather go back on Weight watchers and just lose what's left a little slower.
With regard to Homeopathy in general, it's a bit shady. The numbers on the bottle refer to the levels of dilution. If you put HCG on a pregnancy test kit, it will come up positive, but if it's a homeopathic dilution, it will not. The levels of actual HCG are so tiny that they can't really be measured, so there is nothing stopping people from simply sending you a bottle of water and alcohol. There's no way to know the difference.