If it is coded AZ, I guess it should be fine. There are no statements regarding AirOne per say.....see fine print. What is your fare?

6Alitalia:
Mileage may be earned on Alitalia-coded flights operated by Alitalia or any SkyTeam partner. Mileage credit is not applicable for fares booked in A, R, U, or Z class.

By the way, this post looks eerily similar to another post I saw by you....