Short answer... No.
There are ways of using ftp and going in to the controller, downloading the raw files, and then moving them one by one by hand to the new system, although it usually requires the user to setup their mailboxes anyway to get the placeholder files there first. Basically it unless it is for something very unusual, it's more work than it's worth by a long shot.
Give users a deadline and just say all messages must be retrieved by XX date, then make them set it up new. The hassle just isn't worth it.