There will be mail on the SAFE network. But there is no bridges from the SAFE network to the insecure current internet. To build bridges is to have the very real potential to bring the insecurities and data/identity leakage that plagues the current internet into the SAFE network. For instance an email bridge means that some entity (server/humans) will be able to match up your email address with your SAFE ID, and with all the tracking done because of your email address will migrate to tracking on the SAFE network where ever you use that ID.
So by not bridging then the anonymity features of the SAFE network will allow you to choose how your ID is viewed/used.