The nominal reason for Michael marrying Appolonia was less a rejection of Kay, more that he was hit by the "thunderbolt"--an event of the heart that is hardly unknown even among non-Sicilians, and among those who are already married. Filmicly, it sets us up for the immortal scene with Sr. Vitelli in his cafe (one of the best in the film, IMO); the old-fashioned Sicilian wedding; the film's only T&A scene [humming "Thanks for the Mammaries" ;] and the treachery that led to Appolonia's untimely demise. Symbolically, wedding Appolonia underscored an important milestone in Michael's evolution from rejecting his family and its values (including joining the Marines and being engaged to a WASP); to embracing the family's values (by killing Sollozzo and McCluskey for his father's sake, hiding out in Sicily--and now, courting and marrying a Sicilian girl in the old-fashioned way). Appolonia's death also helps set us up for the cold-hearted, calculating, emotionally limited (and later, emotionally dead) Michael.
That last point falls in with SB's excellent explanation: he was too cold and too self-centered to involve himself with another woman after he dumped Kay.