I don't know if this is the right category but here goes..
We are in the process of moving a number of sites from one server, we have tested with a few test domains including testing with email etc.
One we sent a number of test emails to an account, transferred the account and then waited for the DNS to propagate. Once the DNS had propagated we recieved all the test emails again.
I checked our settings and it was set to 'keep copy on server'. So if there are any users on the server that have this option set I assume it will do the same and redownload all the messages on the server.