To my mind, "science" implies a rational and skeptical outlook. It's the scientific method that is important, not mumbo jumbo.
And the mechanism of verification is important too - you can't just say "somebody knows somebody". It has to be a proper study. If possible, double-blind.
Under those parameters, my hypothesis is that your mantrams will not survive. But those are the only parameters that are worth talking about.
You have indeed brought up a good argument that Homeopathy uniquely treats the individual rather than the disease. Therefore the double blind trials are not an appropriate way to measure Homeopathy's efficacy. This is a valid argument, but then to prove Homeopathy's efficacy, one has to do an elaborate survey that is quite hard to pull off. Selective individual experiences do not suffice. One has to look at all the successful and failure cases in real life Homeopathic treatments and come to a conclusion. I wish there was a study like that. Till then such doubts and questions will linger.
Let us not bring Allopathy into the discussion. This is not about Allopathy vs Homeopathy.