From the TP run wiki:
Upgrading Using Avios (UUA)
Summary guide to bookings which can be upgraded with Avios:
- BA issued tickets (can include other carriers) ^
- TA issued (on BA stock) booking with only BA flights ^
- TA issued (on BA stock) booking with other carriers

- Tickets issued on non-BA stock

TA has to issue the ticket in the country of your BAEC membership as well.
From BA conditions page for UuA:
http://www.britishairways.com/en-gb/...ditions-of-use
The upgrade is a single cabin upgrade from the cabin booked, to the next cabin, this may vary depending on which of BA, AA and IB or a franchise operates the flight.
Upgrading using Avios points on BA, AA and IB Flights are permitted on eligible published fares only (Fare classes are: J, C, D, W, Y, B).
So if you are on a Y booking class on that flight you should be able to UuA in to the next cabin which on a two class AA flight is domestic first. However, won't this be quite a lot of avios to do this?