In most cases no. For students the sharepoint system will use the @rwth-aachen.de e-mail address and for employeers with a so-called TIM-CAMPUS-Link their office e-mail address. For any other people the system will use their contact e-mail address, which is configured at the RWTH Selfservice. As a Workaround you could configure a redirect rule using the RWTH Webmailer, which triggers for the sender "email@example.com" and redirects the messages to an alternative e-mail address.
You can fix any display issues with SharePoint sites after the migration to Sharepoint 2013 through the following actions:
Please go to the "Tools" section in the Internet Explorer, now choose "Internet options" and go to the "Security" tab. Choose the option "Local Intranet" and click on the Button "Sites". You can now add the Sharepoint-URL after clicking "Advanced" in the now opened window. Add the URL of the Sharepoint and apply the changes.
Additionally the option "show intranet sites in compatibility view" under "Tools" =>"Settings of the compatibility view" should be set to true.