Does the poem "The Arab's Farewell To His Horse" by Caroline Norton shed more light on the story "Araby" by James Joyce?

I wouldn't say that the poem "sheds light" on Araby, but there is certainly a connection there.  Obviously, lets start with the title.  Arab - Araby.  The importance to this in both poems is to call to mind the culture of the East, of far away places, exotic places.  The boy in the poem has imagined the carnival to be such a place, exotic and alluring.  "The syllables of the word Araby were called to me through the silence in which my soul luxuriated and cast an Eastern enchantment over me."

Secondly, lets examine the mood of each.  There is a wistful nostalgia and disappointment in both the poem and the story.  Both speakers experience a loss.  In the poem, it is the loss of a most beloved horse.  The speaker says "Some other hand, less fond, must now thy corn and bread prepare,/The silky mane I braided once, must be another's care."  The horse is described in such a way that it seems larger than life.  The same is true of the girl in Araby.  The boy idolizes her so much that he puts her on a sort of holy pedastal.  He says, "Her image accompanied me even in places the most hostile to romance."

However, just as the speaker must give up the horse, the boy is forced to give up his illusions of both Araby the carnival and, through that, the illusion of the girl.  As he sees the petty trinkets and flash of Araby, and listens to the gossipy girl at the booth, he burns with "with anguish and anger."