Cooper would have stuck to his con story as long as it suited him somehow. Having Locke continue to believe he was his father made him vulnerable, easy to use in a pinch. (which he did several times) It also made it less likely that he would hunt him down and take his kidney back the hard way. In the end, Locke's need to believe this monster was his father allowed him to alert Cooper to being found out by his last victims son, so he could murder him. Then he still lied to the police for him. All quite helpful to the con man.