Can homeopathic hcg drops cause dvt and pulmonary embolism?

No: No, it can't. The homeopathic diet aid you're referring to isn't the full strength hormone, it's much less than 1/1, 000 of the normal dose. The only way there would be a concern about DVT or pe would be a rather rare occurrence of clotting and that typically only happens when you get larger doses that react adversely with your hormones as reported at http://www.Drugs.Com/hcg.Html.