If you mean? for Michael to use Kay's WASP “to help "legitimize" himself--his obsession”....
Kay was already Michael's girlfriend, long before Michael having to become the Don and his quest for "legitimacy" "respectability"

• Michael was honest though

I came here because I need a woman, to bring my sons into this world. You'll do -- What's Love got to Do with it?!

Michael had no qualms marrying Apollonia and took longer than a year to contact Kay -- Mama couldn't find Michael a nice Italian origin bride, suitable Mob Boss wife! instead of seeking Kay out