The answer as to whether a DNA test can tell you your ethnic identity? Yes — and no.
We know that, when it comes to DNA, geography matters. Although in principle anyone can mate with anyone else, in practice we tend to mate with people nearby. If we could assemble all the DNA of everyone everywhere, we would expect to find that people living near each other were more likely to be genetically similar than people living farther apart.
It would provide insight for those who have little to no family history. My family barely has any details beyond my grandparents, and even then – I discover that my parents have neglected to mention things.