That is one hypohesis. I am not convinced of it. Anyone can verify for himself that Arawak Indians living in the equator are much lighter than the Africans living in the equator. Similarly the Eskimos live farther north than the Swedes, yet the Eskimos are darker. Whichever the case 2,000 years are not enough. The Afrikaners have lived in South Africa for 400 years and they as white as the Dutch living in Holland.
Secondly the black African Jews are not merely dark-skinned. They have Negroid facial features. When I speak of "Negroid features" I am not talking of skin color. The people of India are brown-skinned but they are Caucasoid.