Setesh:
The error popup that you are seeing only happens in online mode after all the data has been uploaded to the server. You can observe this for yourself by composing a new message, attaching a large file to it, and then watching for transaction logs being generated on the server prior to the message being sent. In addition, the fix described in this blog entry is specific to cached mode, offline mode, and Outlook configured with a PST as its delivery location, so even with Outlook 2003 in online mode you will still experience the same behavior.
A_N_IV:
I believe that Outlook 2003 does have some level of integration with SharePoint to do something like what you are asking for. As for third party solutions, you might be able to find what you're looking for on our partner's page for archiving and compliance at http://www.microsoft.com/exchange/partners/archivingandcompliance.asp.