Henry James's Daisy Miller chronicles Daisy's efforts to construct her own identity in an environment that wants to construct it for her. Despite her death at the end of the narrative, did she succeed or fail in her efforts, or is it perhaps some combination of both?

In my view it's difficult to know if Daisy's intention, as phrased in your question, is to construct her own identity. To Winterbourne (and to James himself as author, I believe) Daisy is an enigma. We cannot be sure if her behavior is a deliberate effort to flout convention, or if there is simply an unexpected (and mystifying) naivete in her makeup as a person that causes her seeming inorthodoxy.
Winterbourne is impressed by Daisy because of her beauty. We can talk all we would like to about his being fascinated by a young lady because of the curiously detached way she acts, and perhaps this is, after all, part of his attraction to her. Her apparent lack of any real understanding of social codes drives Winterbourne on to find out more about her, to grasp the enigma at her core. But he finds out nothing. In Rome her association with Giovanelli infuriates him, as it scandalizes others. He can't figure her out, though the other American tourists seem to take it for granted that Daisy has become Giovanelli's mistress.
When Winterbourne warns Daisy that in Europe people do not understand the sort of mere "flirting" she has been doing, she does not care. Again, we can't be sure if she is deliberately pursuing an independent, novel way of acting, or if on the other hand she genuinely does not know the difference and is clueless about her supposed violation of the laws of conventionality. I would suggest that one of James's themes is that of the uniqueness (for good or ill) of the American psyche. Daisy appears innocent, superficial, and disregarding of others—just as "America" has been and still is perceived by the outside world that way. She does not care if her behavior offends or disappoints those around her. It is possible that some inner guile animated her, but there's no proof of it. There is a remoteness about her that Winterbourne never solves. Yes, she has created an independent existence for herself, given that no one has stopped her and forced her back into the comportment expected of her. In this sense she is a kind of pathbreaker. That she dies at the end is perhaps symbolic of the cold fact that those who choose their own path are usually struck down.