To me, it accomplishes showing the audience that Shadow's not an idiot. It enforces what's said about him earlier-- that he's kept his head done, down his time in the most pragmatic way possible, that he doesn't have an easily riled temper and he's smart enough to know when he's being played, and that all he wants is to get out of jail and see his wife again. All very useful things to get across to the reader.

I'm not sure what you mean by "withholding that information", though. If you mean Shadow's race, the information hasn't been withheld, it's right there and in other places in the text. It's just not explicit. Not everything the author tells an audience is explicit and out there for everyone to see. Some knowledge is knowledge you have to pay attention in order to appreciate. The way I look at it is, a lot of people will miss those clues and assume Shadow's white. Those are precisely the same people who might stop and wonder why they made that assumption, and they might find that exploration interesting.

Or... they might get angry and defensive about it. And that is also interesting.