Could this possibly work?

Well if you can get her to the point where she would accept the fact of being in a relationship with you, I say you should go for it. This also means, I'm assuming, that you're going to have to support her. So I hope you're financially there because it seems like you are already emotional. I don't think her past would come to affect either of you at all. If you accept her for who she is and she has never had that before, then most likely she will never even want to think about her past again because of what she has now. If she's from "the streets" and you put her in the position where she can make something out of herself and be with you for the longest optimal time, then I don't see any reason that she would want to return to her old life. I think it's on the safe side to say that if you like her as much as it seems in this question, you would be missing a grand opportunity to not try to be with her.