Yes, but keep in mind the domain names must match and correct file ownership is required. For instance, you can't just upload those directories from one account and except them to work on a completely different domain name/username combination.
I know this is an ancient thread, but for future reference, there is a way to backup individual emails (or folders).
Launch Roundcube from your cpanel Email Accounts section, and login to your email account you want to backup. Within Roundcube, you can click on each email you want, and choose "More > Download (.eml)".
It may be tedious to do each message, but here is a backup of your mail, preserving the addresses, time, date, and attachments. Save your .eml files, and restore them to another server/address by dragging them into Thunderbird.
Just posting since this thread comes up when searching "backup mail from cpanel".