"Can you persuade me in such a short time to become a Christian?": This remark might have been ironic, expressing a lack of belief. It might have been making fun of Paul, or a dismissal of Paul's challenge. It might also have been a comment on how well Paul could persuade. Or it could have been a genuine question about Paul's intention. It seems best to understand King Agrippa's reply as intentionally trying to avoid the question. He did not want to admit he believed the prophets, because Paul had made a strong case (26:27).
The next step would be to believe in Jesus as the promised Christ, which Agrippa did not want to do. On the other hand, he did not want to say he did not believe the prophets. This would cause his Jewish subjects to feel isolated, and Agrippa wanted their allegiance. His lack of a committed response emphasizes his discomfort with Paul's testimony.