When you send a message from a classmate's profile page, they will get an email saying that you sent them a message. Nobody's email address appears in the email. Instead, there will be a link back to a private message page in which you and your classmate may correspond privately. Nobody else can see these messages.

You can have access to all your private messages in the Message Center (see the link under MEMBER FUNCTIONS) on the left.

On the other hand, if you leave a comment on a classmate's page. Everyone who is logged in will be able to read it. Still, nobody will be able to see your email address.