Correct, although I'm not sure where you will have the opportunity to use a non-AF lounge. There is no arrivals lounge at FCO, and the AZ lounge is located about a mile (I'm not kidding) away from the AF gates at ATH.

If you are flying FCO-ATH, you will have the opportunity to experience the spendor that is the AZ lounge at FCO. FYI, I always use the AF lounge when departing Terminal B at FCO, even if I'm flying AZ. It's a much nicer lounge.