I don't think Rasputin's was one big dramatic act where he pretended that he was compassionate while not actually feeling it. At the very least, I think that he believed that his powers really did come from God and that it was his role in life to help others. I think he sincerely tried to heal these people and help them in other ways. I think that he was sincere in what he told Alexandra and that he believed what he told others as well. One thing he didn't seem to be was underhanded, this is probably what got him in trouble in the end, his unwillingness or inability to pretend to be something he wasn't, even when it may have been in his best interest to do so.