According to the Epilogue, no: in the Siberian prison "he did not repent of his crime," and what makes him sick is wounded pride. What changes at the end is his love for Sonia, not a verdict on the murder, and the book leaves other readings open.
The reading that he does not repent has strong support. Before the court, he says he gave himself up out of frank remorse, but the narrator observes that the answer sounded almost rude, and in the next chapter states: "his pride was greatly wounded; it was from wounded pride that he fell ill." Shortly before giving himself up, he had said to his sister: "I don't think about it and I don't think about washing it off." In prison he takes up the theory again and acknowledges guilt only for not having endured the crime and for having given himself up.
But the text also supports the opposite. At the moment of the crime, the narrator says that, with a clear head, he "would give up everything and go that same instant to denounce himself," moved "only by horror and revulsion at what he had done." On the square, he kisses the earth "with delight and happiness." And if he explains by a dull instinct that he did not kill himself on the riverbank, the narrator suggests another cause: a premonition, already there, of the falsity of his own convictions.
The turn, when it comes, does not come as remorse. On the riverbank, he falls weeping at Sonia's feet, and the narrator says: "In place of dialectics came life." He takes her Gospel without opening it and asks himself whether her convictions might not be his own, at least her feelings and aspirations. The renewal is announced and referred to another tale: confidence that the change is guaranteed, or an admission that the novel does not follow the turn that would save him. In neither reading is the theory refuted: it is left behind, replaced.