As far as I know, members can not see your email adress. I think it's only to register and to recover your password. If you want you can also get alerts that you get on the forum here (replies to messages, PM etc.) in your mailbox too if you enabled that in the settings. Also under the privacy tab, there is no setting that has something to do with your e-mail.
If you want to contact somebody on the forum and talk to him/her or to multiple people privately, the normal way of doing that is sending each other a private message.
Maybe
@Jack can confirm this.