I think that the song's relevance to the story can be traced back to Edna Ferber's fascination and sense of intrigue about the concept of the Show Boat. Consider her own words in this realm:
Here, I thought, was one of the most melodramatic and gorgeous bits of Americana that had ever come my way. It was not only the theater — it was the theater plus the glamour of the wandering drifting life, the drama of the river towns, the mystery and terror of the Mississippi itself.
In this notion, Ferber brings out how the earliest conception of America, a nation that was only about a century and a half old, represented a challenging notion about racial identity. The Show Boat concept highlighted a sense of "glamour" along with a sense of "terror" almost simultaneously. It is here where I think that the song "Ol' Man River" captures this duality in a brilliant manner. The lyrics of the song bring out what it means to be trapped in the complex diaspora of race in America of the late 19th and early 20th Century. Essentially, the song seeks to reconcile what it means to be someone trapped in the midst of this "glamour" along with a sense of "terror." While the singer, a black dock worker, speaks of his own suffering, he is resigned to the fact that the river "jes keeps rollin' along." The fundamental challenge that the baritone, deep voiced singer brings out is how one can reconcile a sense of being where there is so much in way of pain and suffering, and yet there is an almost normalcy about such a state of consciousness. This duality is something expressed in nature, something that the song brings out to reflect the fundamental theme of the duality and complexity of racial identity in America.