I don’t think “Hebrew Israelite” = “Jewish” in the minds of many of the folks claiming to be adherents under either label. But even granting that point it’s not impossible for black folks to become Jewish, just uncommon. A well known example was Sammy Davis, Jr.
Nissim Black is better known these days. He is a rapper from Seattle who became a chareidi Jew.
There’s also NBA star Amar’e Stoudemire, who was exposed as a youngster to the Black Hebrew cult but eventually converted to Orthodox Judaism in Israel.
And there are a few other notable converts to Orthodox Judaism from black or African backgrounds.