Can DNA found on drugs be used as evidence in court or is that unconstitutional? DNA can be transferred from different sources so it doesn't necessarily mean the DNA holder has come in direct contact with the drugs, correct?
Yes, DNA found on drugs could be used as evidence in court, although, by itself, it might not be sufficient to support a conviction.
Generally speaking, otherwise duly authenticated physical evidence is admissible when it is "relevant" and it is is "relevant" when it makes it more likely that an element of the crime (in this case, possession) is true than would be the case in the absence of this evidence. There are specific exceptions that disallow the introduction of relevant evidence, the most general of which is that it would be unduly prejudicial to admit the evidence which is otherwise of only marginal relevance, but in practice, I think that the DNA evidence would pass this test.
It is more likely that someone whose DNA is found on drugs had something to do with the drugs than if their DNA was not on the drugs, even if it isn't absolutely certain that the person was actually in possession of them, so it would be admissible.