No. In my experience all the ancient churches (including the Catholic) do not recruit. They simply reproduce sexually.
Fundamentalist Protestants are very missionary (white on white, Black on Black) but will not cross the color line. And in fact most of these Fundamentalist Protestant "converts" are lifelong believers who are experiencing what in any other tradition would be called a mark of passage.
https://www.google.com/search?q=catholic+church+grew+in+africa&ie=utf-8&oe=utf-8