Our minimum intended functionality is that it will generate and fetch a full account backup then import it using the same logic that we use for backups uploaded by the user. This obviously relies on that functionality being enabled on the hosting package.
It might be possible to transfer the files/databases without generating a full account backup. If it's possible, we will implement it. The same functionality can then be re-used for transferring backups from custom panels, for example Dreamhost or 20i.