I have a familial oral tradition that disagrees with the theory. However, after having met a few "Black Hebrew Israelites" on the street, and having seen their testimony on the internet, I can safely say it doesn't matter.
The dispersal of Israel is a consequence of Deuteronomy 28. This prophecy ends with God gathering his people when they turn their hearts back to him with sincerety.
The introduction of Christianity fulfills this, by mission in England or by chattel slavery in America. After we, or you, or whoever, become Christian, we become part of God's Elect—the newly adopted chosen people.
The result is what matters. The history, while it does show God's hand at work, is irrelevant to our current condition.
Our destiny is tied to yours, just as yours to ours. The old covenant was fulfilled, and that of Jesus's sacrifice took its place.