Facebook to my knowledge does not let you export your friends email addresses in a way that they could be synced with your email service. I think that if they did, it would be beneficial to everyone. Their claim that email addresses are private is bogus. They could add buttons to the privacy settings that would allow a user to block their email from being access by friends. There is no valid, as in non anti competitive, reason to hold on to names and email of your Facebook friends.

I'm just waiting for Facebook to release a real email service ala gmail in the near future to escalate this battle.