If you can book the AA operated flight with a BA codeshare (which it would be if you booked via BA) then it will count as a BA flight for the purposes of the 4 needed.

https://www.britishairways.com/en-gb...ut-tier-points
Eligible flights are defined as those flights marketed or operated by British Airways and those flights marketed and operated by Iberia.

• 'Marketed' means the flight will have a BA flight number (in your itinerary or on your ticket).
• 'Operated' means the aircraft that you travel on is a British Airways aircraft (including franchises and BACityflyer).
• 'Marketed and operated by Iberia' means the flight will have an IB flight number and the aircraft you travel on is an Iberia aircraft (including franchises).