I think you over estimate the ability of a DNA search.
I think if you have already selected someone it might tell you there is a possibility of a distant relationship. But I do not believe it would pull out identities of cousins or the like.
I think there’s a good chance of showing a close relationship. Some traits persist for generations. There is a trait common to Cohen men that can be found in a southern African population that claims descent from that tribe thousands of years later.
Basically, I think it might screen candidates, since they have the names from the letters.