Migration Grunt -
When you login to the mailbox after the mailbox has been moved, you will make a connection to the original mailbox server (presuming this server is still up and running). This server will "know" that the mailbox has been moved (because it can consult the directory and see the updated HomeMDB/HomeMTA). The original server will then "tell" the Outlook client "hey, you're on SERVER-X now" and Outlook will update its profile to reflect this automatically.
So, in short, sure there are things that can break this process. But so long as the original server is still up and running, and so long as the directory is updated and replicating properly, this process should be quite automatic.
Evan