zanna, to answer your question, it would not affect homoeopathic treatment in the way that concerns you.
This is because homeopathic remedies work on the level of energy rather than a material dose. When you take a hom. remedy the tablet itself stays in your body for about 24 hours, but the action of it on you is only for a brief instant, as the energetic imprint of the medicine influences your vitality.
Since homoeopathy does not work on the physical level, the urine is not affected by any "residue" of the remedy left in it.