Creating mailboxes this way does not store the mail on the iPad.
Your best bet to save your mailboxes from your MobileMe account is to migrate to iCloud. If you have local mailboxes on your Mac, you can create a new one in iCloud, then move the emails to them. It might be possible to move the entire folder. This might take a while.
Yes, mail counts against your iCloud storage. However, if you are already paying for a MobileMe account Apple gives you the equivalent extra storage automatically. It will need to be renewed roughly the same time your MobileMe account would have been due. On the other hand, 20GB of extra iCloud costs $40, less than half what it cost under MobileMe.
Once all your email is in iCloud, it will be easy to get it on the new Mac, by simply adding your iCloud account. Then is if some of the archive folders are cramping your available space, you can copy them back to local folders on the computer.
That is one way.
The other is to make archives of you folders on the Mac now, save them on a USB Drive or CD, then import them when the new Mac arrives.
At any rate, you're going to want to migrate off of MobileMe, and soon. Do it while you'll have time to make sure you saved everything you want.