This isn't about Ansem, it's about how Kairi may leave DI in KH2.
Let's keep this on topic.
I don't think that Kairi would leave the island at all, unless Sora came back and brought her. Although, there is a quote in Deep Dive/ASAS that says "This time, I'll fight," and it can be assumed that Kairi says this.
So who knows? Or maybe, she's on the island and has to fight her own battle.