You can upgrade an AA marketed, BA operated flight, but it has to be booked into full fare J, D, or R. The most common discount business fare class of I is not eligible. A quick look on Matrix shows the fare difference between the cheapest business and the cheapest "full fare" business tickets on a 7 day return in September is around $1300/ticket. I'm not sure that it's really worth the fare difference plus 35K miles each for the increase in service on a 7.5 hour overnight flight. But that's just my take...