It's just an idea, I have not tried this, but you could use the mailsorting contrib from dungog
http://www.dungog.net/wiki/Smeserver-mailsorting and create some procmail rules.
I have an SME server setup in a school to retrieve all the admin emails from their SUSE based server, and use the procmail to send the rejeceted emails on to the correct users back to the SUSE server, as there are a lot of emails from mailing lists people are on that get rejected by the SUSE and thus end up in the admin mail box. I use the SME to sort based on recipient, subject or 'email headers' and forward on to the respective users mail boxes. It seems to work quite well for what I want.
Alternately, set up your email client to get the mail as a pop3 account in addition to your main email - if you're inside your corporate network, this could be OK. If your corporate email server can retrieve email from a POP3 server, you may be able to get it to retrieve from your SME. MS Exchange can do this, and forward all mail to a specific user mailbox.
I guess the other possibility is to use the email delegation feature of SME to send the email upstream, but this may not work if email is passed without the date headers.