I think that the statement is valid. One of the most powerful elements of Steinbeck's novel is that the work speaks to what it means to be alone and to be alienated. All of the characters experience this in different ways. Lennie is not the only one whose dreams get the best of him. Candy hopes to be included in something, anything, that is different from the life he currently leads. Crooks struggles with trying to dream and living in a condition where a person of color is not allowed to dream. Even Curley's wife envisions a life that is radically different from what she lives. The tragic condition in the novel is that what happens to Lennie happens to all of their dreams. The novel speaks to the crushing chasm between reality and a life that is different from the dreamsof life.
Consistent with the social realism of Steinbeck, the world in which the characters live is one where there is a great deal of harshness and disinterest. It is because of this that this world gives impetus for the characters to dream, to envision something different from what is. While Lennie might be motivated by "pettin' rabbits," it is no different than Candy's desire to own something that is his, or Crooks' hope to have company, or Curley's wife's desire to be in "pitchers." In the end, all of them suffer the same fate as Lennie, reflecting that America's image as the land of dreams can prove to be the image of where dreams are crushed.