The question seems to be "Did Noel kill himself at the end of Suskind's The Pigeon"? The short answer is that we do not know.
The Pigeon is about the alienation and disconnectedness Noel feels in relation to people and the world. He has arranged his life so that he can avoid any form of human interaction outside of his work life as a bank guard (which, frankly, is in a profession that values detachment).
When he encounters the pigeon, he immediately feels discomfort that his solitary life has been disrupted. The pigeon represents the outside world and the inevitability of connection, even when one chooses to disconnect. It jars him so much that he plans to kill himself the next morning (death, of course, being the ultimate form of solitude).
When we last encounter Noel, he is smelling coffee from a neighbor's apartment. He seems to have accepted that he is not alone because, despite his belief that human relationships have no value, he is involved with humanity. The pigeon, the people he works with, the neighbor making coffee—all represent the essential futility of, and perhaps the unhappiness of, isolation.
We cannot know if he kills himself, but he seems to inch ever closer to embracing connections, to recognizing that involvement may be a path toward fulfillment.