You will get miles even booking directly with Alitalia. Just add your Skymiles # during the reservation. And it should post to your DL account within a few days or weeks of the flight. Now, do save the boarding passes after each flight because if for some reason there is an issue with the miles posting to your DL account, you will need the boarding passes as proof that you flew when you submit a mileage request. While I haven't booked AZ, I've booked multiple Delta partners via the partners website and the miles have credited over to DL, including AF/KLM, Virgin Australia, & China Airlines.