Hi,
This is far fetched, no Idea if this might work or not, never tried, not gonna try it.
Mails are stored in /home/user/imap
If you can somehow make the permissions in those folders so that the users can't write, but only read (r-x).
altough, I wouldn't try this on a user / mailbox that you intend to keep, try it first on a test user.
Right know I can think of problems with clients not being able to set a mail as read, there are probably also going to be other problems with imap clients.
Wouldn't recommend this, and maybe there is another solution to your problem.
regards,
Stijn