From what little we actually see of mirror Kirk, it seems clear that he is basically an inhuman monster who would never follow Spock's plans to reform the Empire.
As for the fall of the Empire...
Spock planned that all along. He wanted
the Empire to fall, so humans would see what it's like to be oppressed - and thus make sure it never happens again. Spock had the whole thing planned out from the get-go. He would, wouldn't he?