It should, but it is up to each character to discover how living in one's own house would accomplish his or her dream. It obviously fulfills Mama's because she'll have a place in the sun where her children--just like her plant--can expand and not be stifled. For the rest:
1. Beneatha: Throughout the play, Beneaths is searching for identity. She flits from one interest to another, from one man to another, hoping that she will discover who she is and where she should be going. If Beneatha is able to live in a house which she knows belongs to her family, she will have that as a starting point for her own path in life. She most likely will no longer have to share a room with her mother or fight numerous people just to use the bathroom. She will know that there is always a permanent place for her to return to.
2. Ruth: A house will give Ruth's growing family the opportunity to expand. She can nurture her children in a place free of rats. She will have room to develop her relationship with Walter and a place besides a couch for her son to sleep.
3. Walter: Walter's dream would not be completely fulfilled by the house unless he matures. Walter wants to own a liquor store because he wants to be his own boss and get out from under "the man." If Walter realizes that by investing his deceased father's money in a house he is investing in his family and taking them away from white landlords, etc., then he most likely will see his dream's attainment. Owning a house could give him the ability to strike out for other dreams.