Can a homeopathic remedy show a false positive in a drug screening?

It's extremely unlikely, because of how homeopathy works (or, more accurately, doesn't work).

Homeopathic remedies (note that I am distinguishing them from "naturopathic" remedies, which in some cases can and do work) are made by taking an extract from ... something. It doesn't really matter what it is, because whatever it is is then diluted to the point that it may be statistically unlikely that even a single molecule of the original substance remains. Homeopathic "remedies" give concentrations like "10C". This means that the starting material was diluted by a factor of 100, and then a sample of that was taken and diluted by a factor of 100, and this was repeated 10 times for a final concentration of 100,000,000,000,000,000,000 times less than was in the original sample.

Couple that with the homeopathic belief that it works better the more dilute it is (many homeopathic remedies start off with things that are poisonous, so this belief is really a good thing ... it keeps homeopathy from actually killing people outright), and you should see why it's not likely that what is effectively sugar pills or water is going to cause a false positive for anything.

Even if the starting material was pure whatever drug is being tested for, it's unlikely that a homeopathic mixture with such a dilution factor would even register on the test, and even less likely than that if it was some other compound.