If Michael was in Part IV it would be the time before he dies. There's roughly 15-20 years from the opera to the time he dies at the end of Part III.

And I wouldn't count on Michael wanting to have anything to do with the business after seeing Mary killed before him and losing Kay again.

Vincent could want to have him as consigliere, but I would think that Michael would either return to Sicily and live out his days there, or never go back to America and live his final days as a hermit in Sicily.

Part IV would be a stretch and become too much like the Sopranos... I am against it, but would still go see it if they made one.