Dave Noble, once again the T&Cs say nothing about the process... It only says that code share flights are eligible. So, if you book an AA code share on BA in an eligible class you are allowed to upgrade that flight. How it's done should be of no concern.
Let's look at the process:
A passenger is booked on AA6148 in 'B' class from LHR to EWR. He wants to upgrade to WTP. 'B' class is eligible on AA code shares. He calls an agent and says that he wants to upgrade. The agent first re-books the passenger onto BA185 in 'B' class and then upgrades him into 'P' on BA185. Now, the passenger does not need to and won't know this process but when he receives a new e-ticket he will be booked in WTP on BA185. Was the code share flight upgraded? Yes, it was. The only difference is that now the passenger is booked on the prime BA flight number because the prime carrier is handling award space, and AA6148 would not have any award buckets. The passenger will receive mileage according to the originally booked flight (AA6148).
So, no the flight does not have to be booked as a prime BA flight in order to be eligible for an upgrade and AA code shares are eligible but how it's done is a different matter.