Regarding predecessors, it wasn't at the same level of immersion, broad talent or personal response but early sides by The Righteous Brothers were an absolute staple of black radio in the early '60s when that "reverse cross-over" was pretty rare. But their material went down-hill pretty quickly.
Earlier the only example I know of someone who literally chose to "become black" in music was Johnny Otis - who was a Greek-American kid from Berkeley. In his teens he married his black sweet heart, traveled with all black blues and "territory" swing bands in the late '30s and early '40s, was totally immersed in black culture and music and had a string of big band, early R&B and R&R hits via his own band and singers he promoted like Big Mama Thornton, Esther Phillips and Etta James.
But Johnny basically claimed blackness in a pre-civil rights world when you couldn't live and move across "color lines" without making a life choice and sticking to it - he was simply considered black, even making the cover of "Negro Achievements" magazine in the early '50s, and was deeply involved in SoCal black political activism. I've talked to older black folk who saw his band at the Apollo in the 40s and early 50s and didn't have any idea he was white.
I caught some justifiable heat for linking to Teena Marie's more pop joints, but I refuse to front--I'll take The Righteous Brothers version of "Unchained Melody" over Harry Belafonte's. There. I said it. Ghost ruined that song.
There's also some interesting conversation here about how black people have thought about white people who've done the reverse cross-over. As is mentioned in the comment, this deserves to be bracketed off from simply singing R&B, or performing blackness. It's interesting that Brucds notes that many people thought Otis was black. I can totally see why. Pictured above is Abe and Effa Manley, co-owners of the Newark Eagles. Again, I would not have known this, but Effa was white--but had a black stepfather and was thus considered "a light-skinned black."
I think what all of this really is how much blackness, like any culture, really isn't about a melanin count, per se. So much of it is historical along with specific mores. It's no mistake that both Manley and Teena Marie grew up around black people. Johnny Otis claimed to be "black by persuasion."
You look at this people's lives--Manley was the first woman inducted into the baseball hall of fame--and it's kind of humbling. It's like, I'm the descendant of slave, they aren't. But really, if Teena Marie says "I'm a black artists with white skin" who am I to truly object? Johnny Otis was on the cover of Negro Achievements. That's more than you can say for the kid.
Also, Questlove, for a less poppy perspective, Questlove breaks down his Teena Marie favorites.