I expect the story would have been very different. First of all, KH2 would have begun soon after COM and there would be no 358/2 days. Sora, Donald, and Goofy probably would have met up with Diz, Mickey, and Riku not too long after Riku fought XH.
Xemnas would be trying to get both Xion and Roxas to pledge absoloute loyalty to him so he would have 2 keyblade weilders to combat SRM.
It would be a more tense situation for Organization XIII than KH2 was. Roxas and Xion would probably refuse to join with Sora but may later on help him defeat Xemnas once they discovered how evil Xemnas was. Axel would of course follow Roxas and Xion and join Sora's team.
The organization would use Kairi as a hostage but since Sora does'nt remember her it might not bother him, however it would bother Riku and Mickey and once they explain things to Sora, he would be pissed at the organization.
So after Xemnas is killed, Kairi would be hurt that Sora forgot her and it would end as a bitter sweet game.