Keep in mind that to someone totally untrained in science, "a scientist says" is not that different from "a priest says" in terms of asking them to take something on faith. As level of scientific training increases, this changes somewhat, as we begin to understand that "a scientist says" carries a certain implicit claim as to the experimentation that went into the discovery; but even then, it's important to remember that much of what you and I _know_ about science we know because some authority figure told us. We may have chosen our authority figure wisely, but that's still what it is: do you believe light travels through a vacuum, or through a mysterious lumeniferous aether? Why? Is it because you did an experiment? Can you even explain what the experiment is?

As for me, I learned it in class and read it in a book. A lot of the "convince people of evolution" argumentation is focussing on entirely the wrong level of instruction, because it's asking people who learned one thing in class and read it in a book to instead believe a different thing that someone else learned in class and read in a book. Local evidence is no help either, because it's going to be anecdotal, and a lot of nonscientific arguments (including religious ones) can marshal evidence too. The problem is not convincing creationists to believe in evolution; it's not even convincing believers in one authority to believe in a different authority (which, while solving one immediate problem, just defers and sets up a different one). The problem is in convincing people of the scientific framework in the first place.

So no, DNA wouldn't do it.