DNA Analysis Prove This? (Suspected Sephardic Ancestry)?

My wife is from Brazil. Her ancestry reads like the United Nations-she has Portuguese, Dutch, Swiss, and French forbears. In any event, her sister is convinced that a Great-Great-Great Grandfather was a Portuguese Jew (marrano), who left the island of Curacao, sometime at the end of the 18th century. Their reasoning is that the man adopted a new name (Carneiro -“Lamb” in Portuguese) upon entering Brazil. I understand that DNA analysis can reveal certain ancestries-is this the case?

With two exceptions, a subject’s Great-Great-Great Grandparent has only 1 chance in 32 of contributing a given subject allele, and I think that’s far too small to make such a test useful.

The exceptions are the subject’s mother’s mother’s mother’s mother’s mother, who contributes the mtDNA, and a male subject’s father’s father’s father’s father’s father, who contributes the Y-chromosome. Only the latter could apply here, if Carneiro is the purely patrilineal Great-Great-Great Grandfather. Even then, you’d need to test your wife’s brother (or uncle, etc.) since your wife doesn’t have a Y-chromosome!

Most Sephardic Jews are in J haplogroup. The test could give probabilistic evidence, but wouldn’t be conclusive since many Jews are not J and many J’s are not Jews. (Moors are also commonly in J haplogroup.)