When thinking about literature, I tend to try to avoid the whole question of "intention." Two New Critics -- last names Wimsatt and Beardsley -- wrote an influential essay titled "The Intentional Fallacy" that outlines several reasons why the author's intention should play no role in how we read works by that author. I'm not at all a New Critic myself, but I think they're right when they point out that the author's intention is neither available nor desirable.
Having said that, though, I'll try my hand at answering your question. Because the novel was published in New York in 1912, it may have had some black readers but was probably purchased and read by mostly white readers. Perhaps the intended audience was the Northern white reader who liked novels with a little mystery or scandal, who was generally sympathetic toward blacks (at least in the abstract), and who might be interested in getting what seemed to be an educated insder's view of life as a black American. Much like the narrator, as he grows up and moves from place to place, the reader is slowly educated about racial discrimination and about the living conditions of poor African Americans. The novel (or the author, if you prefer) does not assume that the reader already knows all about these things.