Why wouldn't you? What in specific are you afraid Facebook will do that Google would not?
This seems like pure knee-jerk "facebook = privacy problem" thought to me. I can't imagine Facebook making your emails public any more than I can imagine Google doing it.
I know gmail scans my message contents for contextual advertising, but it would never surprise me if facebook subsequently sold my email address to advertisers based on the content of messages, both current and historical.