Horde is just a webmail interface, nothing else. Plesk uses qmail for e-mail. If you have Red Hat as your OS, the mail dirs will be in /var/qmail/mailnames
I'm sure you could convert the existing e-mail contents from your previous server, but there is more to it than that. You'd also have to make a script to create all the mail boxes (users, passwords, etc.) in Plesk. Plesk has command line utilities that are nicely suited for the job, though.