Yes, DNA can identify a distant relative. Looks or appearance is a manifestation of information encoded in three nucleotides in sequence, for example shape of lips. Such nucleotides are heritable since they are contained in the chromosome that are carriers of heredity. Some nucleotides in a gene pool, meaning a clan, are identical, others are not. Identical nucleotides, for height for example, can be found by DNA test. In identical twins a lot of genetic information (three identical nucleotides in the same sequence) are common to both. Not so in fraternal twins. Identical twins are virtual clones though since they had been fertilized by one "seed." Fraternal twins had been fertilized by two separate "seeds"; they are a brother and a sister born in immediate sequence.
For example, the amino acids guanine (G), arginine (A) and thymine (T): a sequence of GAT produces one kind of protein, the sequence AGT produces a different protein. These proteins compose the body.
I have a Hub "Why Criminals Cannot Fool and Escape from DNA Fingerprinting" that gives more details.
Bobby Fischer was reported to have a child by a Filipina. So the child was DNA tested. If she were Bobby's daughter she would inherit a fortune (largely the prize money in the Fischer-Spassky chess match held in Czechoslovakia)as Bobby had died in Japan.