Ya, you can grow them
Together, only thing is the auto doesn’t need a light cycle change to 12/12 to start flowering and the female will. You will need keep it on a 12/12 light schedule for the entire flowering do to the female. With just the auto you could leave it on a 20/4 or 18/6 schedule and buds will still happen. You may get a better yield on the auto doing it separately because of this. Cheers💨