Catholics: Would your faith be shaken if the pope was brazenly immoral?

Although I respect the pope, I look at him as a person and not infallible. If he was a corrupt person, I would be disappointed in him and surprised that he would have bothered dedicating his life to religion. I wouldn't say my faith would be shaken though because to me religion is about believing in God and listening to him to help me try to be a good person. That said, I am by no means a strict Catholic and I imagine others who are more strict followers would probably feel differently.