Gregor,
The most likely outcome of running the migration multiple times is that data will be duplicated in the new mailbox. Between runs, the migration utility does not keep track of what data has been previously retrieved. The migration utility does have the option to delete all items before the migration, but using that would be just as effective as running the migration once.
As Gabriele suggested, you could do a migration of the Calendar, Contacts, and Notes using EWS, then set up message retrieval using either EWS or IMAP.
Ultimately, if a more gradual migration is a viable option for you, I would do as Brian suggested and make sure mail is being delivered to the new server before configuring the migration from the old server. Then you don't need to worry about new data coming in during the switchover.