Although I have turned off the ability for my users to see the archives until its restricted so that only members of a particular group can see messages sent to that group, I did a little test.
I have an alternate email address set up and I sent a message, from that alternate email, to a group that I belong to. The message went through fine, I got it in my primary email as coming from me - showing my primary address as the sender.
BUT when I went and looked at the archive of messages sent to that group, it shows the message sender as nothing.. a blank space.
I think this field needs to be the primary address of the sender. Obviously a LOW priority bug.