All the accounts on the plesk server can use any domain hosted on it to access their mail (i.e mail.theirdomain.com,
www.theirdomain.com,
www.ourdomain.net, mail.ourdomain.net etc). Mostly they use mail.ourdomain.net though. A mail.whatever.tld is set up automatically with all accounts and mail.ourdomain.net is just one of those subdomains. ourdomain.net is a standard hosting on the account like all others.
The problem is that if a message is sent from the mailserver which still has the older DNS/MX records cached then that mail will be picked up by the plesk server. If they then download their mail from mail.ourdomain.net (which would now be pointing at the new server) then they will miss that message.
At the same time if someone is on holiday for example and downloads their mail from mail.ourdomain.net (now at new server) then any mail which was picked up by the plesk server would also be lost.
If there was a way of downloading the email via pop3 (like an exchange server for example) then it'd get around this. The other alternitive would be if we could download the mailbox files from the plesk server and then upload them to the Cpanel box.
As an aside, it's fantastic to have someone 'offical' answer the question! I'm a fan of cPanel and have all my own boxes running cPanel. This is just on behalf of a design company I do the tech for too. I've been badgering them to migrate to cPanel for a while now so need it to go right!