I don't think there is enough evidence in the novel or film to support a contention that Michael would have continued as (or become) mafioso before Appolonia's death. Her death soon after Sonny's murder probably embittered him. Michael murdered Solozzo bcause he was a threat to Vito; Michael sought revenge for Appolonia and Sonny.

Kay had nothing to do with Michael's motivation for legitimacy. As I and others have opined, Michael's concept of legitimacy was different from most peoples. Kay was simply an accoutrement; she was utilized by him to achieve his version of legitimacy.