You would have to setup impersonation in ECP to make this happen. If you are setting up your own account to do the imports yourselves, then yes you can setup a global account with application impersonate. If you are wanting to give a customer an account then you would need to limit the RecipientScope to the organizational unit or distribution group so they can't impersonate other accounts.
Also MigrationWiz defaults to delegated access. You have to go into the settings in MigrationWiz and tell it to use impersonation.