No, they don't. Homeopathy "works" on the principle that water can be "imprinted" with something that makes you ill. You then dilute the water literally billions of times until there is no trace of the something that makes you ill, and just the imprint left on the water. This imprinted water then somehow helps to cure you, on the strange assumption that "like cures like".
The most obvious problem with this is that all water in the world ever should now arguably be imprinted with everything in the world ever, but they get around that by saying they use "succussion" to control which imprints remain.
It's ********.