I think that I would have to offer up some level of resistance to the question on two levels. I am not entirely certain that Steinbeck is directly speaking of the immigrant experience in his work. The experiences of the Dust Bowl as well as what constitutes the American Dream is written from the point of view of those who lack social, economic, and political marginalization. The individuals Steinbeck depicts in this struggle are not immigrants but rather people who were born in and have lived in America. In this, Steinbeck might be pointing out how individuals in the position of marginalization struggle. While this can be extended to the immigrant predicament, I don't see this as Steinbeck's primary focus.
I think that I would probably voice some level of divergence on the notion that the American Dream is "unattainable." I think that Steinbeck is too much of a believer in social realism and the power of transformation to write a novel that depicts so much to simply capitulate to the idea that the American Dream is "unattainable." Certainly, he writes about the struggle that is in America of the 1930s. However, one of the major themes of the book is the power of hope and the belief that individuals do have power and autonomy to transform what is into what can be. Ma Joad is a firm believer of hope and believes in the collective vision of success, despite the hardships that are visited upon her family. At the same time, the presence of Jim Casy as well as how Tom absorbs these lessons, committing his life to them, reflects how there can be a vision of the American Dream that seeks to bring a better life to others. Finally, the sacrifice that Rose of Sharon makes at the end of the novel does reflect that while the vision of the American Dream might be difficult to achieve, there can be satisfaction in ensuring that individual self- interest does converge with collective betterment, making the dreams of America and of Americans something that is evident. I guess I could see how the novel does show an "unattainable" quality to the American Dream, but there are too many signs of hope and collective betterment to simply ignore. A vision of the American Dream is present, different as it may be from a more mythological vision that has been presented.