It couldn't be the Qantas brand. The various awards are quite specific. That's why the 717 operation will always be Qantas Link. Change the name on the side of the aeroplane to Qantas and it becomes subject to the various Qantas awards.
So sure, they could operate the A320s under the link banner if they want to but I'm not sure they can have it as Qantas with an 'operated by' for australian domestic services.