Opinion question: if Fredo hadn't slipped up, would Michael have ever known of Fredo's connection to Roth, and the assassination attempt?
He would have slipped up sooner or later--probably sooner. But even before that, Michael still would have been obsessed about finding the traitor in his family. Even with Roth dead or on the run, the traitor would still be a threat to him. His suspicions wouled have led him to Fredo eventually.
