That's not how private_network works. It will always create an extra interface. Vagrant needs the first interface that comes up to sit on the management_network so that it can connect to it and manage the VM.
No, because it is entirely against the design philosophy. The management network is there to allow Vagrant access to the VM and by not using DHCP we cannot know the IP address of the booted VM because we cannot alther the box VM network configuration until after it booted.