What role does the electric organ play in Norma Jean and Leroy’s relationship? Does it in any way influence the breakup of their marriage?

In "Shiloh" by Bobbie Ann Mason, there are a variety of things that contribute to the breakup of Norma Jean and Leroy's marriage—his insistence on building a log cabin, her commitment to bettering herself, and so on. While it does give the reader insight into Norma Jean's emotional state at various points in the story, the pipe organ does not directly influence her decision to leave him. Additionally, you can't ignore a few of the song choices, which end up being a subtle way to foreshadow the end of the story.
"Shiloh" follows Leroy as he attempts to pick up the pieces of his broken marriage after years of being on the road as a truck driver. While he deals with his perceived inability to work, Norma Jean begins her journey to improve herself through work and school. The main driver of Leroy's actions, the idea to build his wife a log cabin, becomes an obsession and is symbolic of just how out of touch he is with Norma Jean. She wants to move on with her life, while he has become reminiscent of all the things he missed while he was on the road. The log cabin is his way of giving them a fresh start, something she eventually admits she "can't face . . . all over again."
At Christmas, Leroy buys Norma Jean an electric organ and reflects on how she used to love to play piano. She indulges him from time to time, belting out songs like "Can't Take My Eyes Off You" and "I'll Be Back." These two songs speak volumes about their marriage. The first is a love song, and it symbolizes a happier time in their marriage. The second, however, foreshadows the end of the story. Leroy looks at the song as a symbol of his new life at home, though in Norma Jean's case, it has a much deeper meaning. Two of the lines in the song—"I want to go, oh / But I hate to leave you"—perfectly sum up her feelings about Leroy. At this point in the story, she has not left him; however, in a way, her drive to better herself begins to lead her away from Leroy, who is simultaneously stuck in the past and looking forward a future that she does not want.
Later in the story, Leroy relaxes while Norma Jean plays "Who'll Be the Next in Line." This is a huge sign that all is not well between the two. The song is about making mistakes in love, asking, "Who'll be the next in line for heartache? / Who'll make the same mistakes I made over you?" While this may or may not be a conscious choice on Norma Jean's part, it cannot be overlooked—especially when considering how the organ influences their marriage.
Overall, the pipe organ does not directly impact Norma Jean's decision to leave Leroy. Their marriage is ruined by a host of other things, such as his reluctance to build a life with her (as opposed to a cabin) in which she can be happy. However, it does give insight into her feelings toward her husband, and, as said before, some of her songs foreshadow the events at the end of the story.