Willy Harris is actually an incredibly important character to the play overall, because it is through his deceit and treachery and the way that he runs away with the money that Walter gives him to set up a liquor store that Walter is able to finally find it within himself and this failure to become a man and take a stand for his whole family against Lindner. Note how, in the final scene, before Lindner enters, Walter looks as if he is going to take the money that Lindner is offering. In spite of Mama's words that nobody in their family had ever "let nobody pay 'em no money that was a way of telling us we wasn't fit to walk the earth," note what Walter says and how he justifies his position:
I didn't make this world! It was give to me this way! Hell, yes, I want me some yachts someday! Yes, I want to hang some real pearls 'round my wife's neck. Ain't she supposed to wear no pearls? Somebody tell me--tell me, who decides which women is suppose to wear pearls in this world. I tell you I am a man--and I think my wife should wear some pearls in this world!
Interestingly, in spite of this speech and the unfairness of the world that it points towards, the final realisation of Walter that he is a man, in spite of his mistake and foolish decision to give the money to Willy Harris, is what gives him the power to reject Lindner's offer and to assume the role of family head that Mama has recently relinquished. Thus we can see that, although Willy Harris never actually appears in the play, he nonetheless plays an incredibly important role.