I'll keep this very brief here and say just this:
When our narrator is singing, we start in the present, the words have meaning for us in relation to our current social circumstances (e.g., High Water and September 11th). And we experience the statements of loneliness or anxiety or rebellion in that context. But, when we learn that the narrator is either speaking in Timrod's or Ovid's words, or has been replaced by Timrod or Ovid in the song, if we recognize that shift in narrator, and know the the overall sense of the original poem that the lines come from, and if we know the historical conditions in which the "quoted" lines were written, then we can overlap Ovid's or Timrod's experience as well as all the implications of the Civil War or the collapse of Rome onto our 21st century narrator. Suddenly, Dylan's narrator is telling us that what looks like an ironic or smirking crack about our times is, in combination with the incorporated lines (and the world they bring with them), in fact a statement of a coming catastrophe or of a sense of a deep corruption, or a kind of loneliness that isn't possible to imagine in our times anymore.
A nice example of how being aware of a source can add to the listening experience.
Was listening to Things Have Changed
When I hear the one line: "Don't get up gentleman, I'm only passing through"--the entire text of A Streetcar Named Desire begins to have a conversation with the rest of the song. A person in an extreme mid-life crisis, Blanche (reflecting the Michael Douglas character in Wonder Boys, with a similar love for escaping through the bottle) is being led away by a kind doctor on her way to the mental institution--she's out of her mind at this point ("people are crazy"), but still putting on the airs of gentility. Tennessee Williams' plays are about sensitive souls that cannot survive the brutality of the world--which crushes the fragile. Williams' characters often attempt to wear the mask or play at a role to cover up or protect vulnerability ("I hurt easy, I just don't show it" and "I'm trying to get as far away from myself as I can.") What "I'm only passing through" means to these "gentleman" at the end of Streetcar as they are playing poker ("you can't win with a losing hand") is different for each--but mostly Blanche's line is met with indifference ("I used to care"). New Orleans, desire, the Tarantula hotel, trains and streetcars--it all happens in the blink of an eye when I hear the line.
("Passing Through" is also a folk song by Dick Blakeslee. Later sung by Pete Seeger for Henry Wallace's 1948 presidential campaign. It was sung for unions and at political rallies (and The Highwaymen, Cisco Houston, Earl Scruggs, Leonard Cohen all later covered it as well). It contains the repeated phrase: "I'm only passing through
." The reference conjures up a time and an era when "I used to care, but things have changed.")
There are likely (I have no idea) a number of other lines from the song lifted from other sources. I don't believe these lines are randomly tossed together, drawn from a hat and arranged to rhyme. But I don't think that knowing the references is at all essential. The feeling and meaning of Things Have Changed comes through whether I know Streetcar or not (or the folk song). But for me it can make the listening experience richer.