My understanding is that it will need to be rebooked onto the BA flight number in order to get access to U class inventory and that ( unless things have changed ) that the upgrading of the codeshare is only theoretical at this time since AA offers no award inventory on the AA codeshare

Whether this means that the upgrade will be scuppered on the corporate booking , I am unsure. AA shouldn't be modifying agency bookings generally iirc. If it is on an 001 ticket and AA can reissue it onto the BA flight number you may be ok. Do you have any AA domestic sectors in the itinerary?