Yes - if a person purchased a J afre and then is booked in economy due to it being either an economy only flight or becuase J had zero availability, the booking class that the passenger will be booked in will be Y

If it is a discount business class ticket, the booking class may be a different economy booking class

If the passenger is booked into J, then that passenger is booked in business class

When checking fare details, such as offered on Expert Flyer, there is information on what booking classes may be used

The fare basis will stay the same

e.g. booking a fare basis JRT for A-B-C r/t but J not available from A-B , then ticket will reflect

A-B - Booking class Y Fare Basis JRT
B-C - Booking class J Fare Basis JRT
C-B -Booking class J Fare Basis JRT
B-A - Booking class Y Fare Basis JRT

If J becomes available for A-B , either due to improved availability or due a change of aeroplane that means that J is offered, then can change to J on the A-B by phoning the airline and getting rebooked into J on A-B . Will then be able to select seats in the business class cabin

The ticket will need to be revalidated or reissued ; AA seems not to be in to doing revalidations though