I don't think Ansem the Wise is her father, considering she lived with her grandma I think it would make more sense that Kairi's mom and dad were King and Queen, making her a princess, and they died premature and she went to live with her grandma, where Ansem the Wise was elected as ruler democratically. She may have crossed paths with him but I don't think she knew him personally. But Nomura does love to surprise.