Yes. The narrator is close-minded, fearful, judgmental, prejudiced, possessive, and unfriendly, not to mention a substance abuser; these are not generally attributes viewed as heroic. That said, the narrator does have positive qualities, and most of his negative characteristics seem to come from a fear of being abandoned/alone and his frustration re: his inability to express himself. For instance, he obviously loves his wife. His seemingly callous reaction to her suicide attempt covers up his deep-seated fear of losing her. He seems to have based his whole life around her; he doesn't have friends, and he is so focused on her that he tells us much more about her past than his own. He is jealous of her first husband, and also of the blind man; the blind man has an intimate relationship with his wife and can communicate with her more more easily than the narrator can.
The narrator gets stoned and drunk. This inebriation allows him to let down some of his defenses so that he can help the blind man experience the cathedral; the wonderment that he feels seems to hint at an underlying urge to understand the world and to learn to communicate with and connect to other people. The cathedral itself (the most important symbol in the story) has various meanings. One of the things it represents is grace/redemption, and that's just what the narrator seems to want, whether he will admit it or not. All of these small details hint that he is more sensitive and loving than he may first appear.