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.
Traits are not the same as DNA ratios of base pairs of the 46 chromosomes.
As I understand it, if you had someone you already thought was a cousin, DNA testing would show the likelyhood that they were related.
But it is not going to pull those relations out of a larger database. The combinations and possibilities are too immense.
DNA Identification Technology
http://dna-view.com/DNAtechID.htm#kinship