The simple answer is no: one cannot say that Wiesel lost his humanity. The extreme suffering inflicted upon people in the concentration camps was intended by the Nazis to dehumanize them. But in my view, Wiesel's narrative shows that this did not happen.
Eliezer's life in the camps revolves around his father and his wish to protect his father against all odds. The appalling conditions of terror and fear are calculated to create an "every man for himself" situation, but Wiesel and others resist this and continue to feel empathy and solidarity with the other victims. However, it's impossible to avoid becoming desensitized, to some degree, to the death and suffering surrounding everyone. Elie realizes that he cannot help thinking his father has become a burden and that his own life would be more sustainable if his father simply were not there. The words "free at last!" occur to him when his father is finally gone.
Eliezer, all along, has felt tremendous guilt about this emerging realization. If anything, this is a sign that he has retained his humanity. But in general, a numbness to the relentless cruelty around him has set in. At the end, after liberation, he essentially feels nothing, least of all the presumably expected joy of freedom. He sees himself essentially as one of the living dead, saying, "From the depths of the mirror a corpse stared back at me."