You can configure a filter following something like this
http://tinyurl.com/ylrrjcf
to bcc to a remote mta with a fixed mailbox. You just need not to include rule with specific rcpt.
But in my opinion, you should just archive it and let your linux box to scp the archive file regularly. They are nicely stored in mbox format and rotated. As long as you copy the archive soon enough, you wont miss any mail.
i.e.
Log-Alan-All-Mail:
if (recv-listener == "InboundMail"){
archive("all-outgoing-mail");
}
Chris