This can be done as others have noted above. However unlike AA's upgrade "waitlist", if you want to upgrade on BA using Avios, you have to constantly check upgrade inventory and call BA right when the upgrade seats open up, as BA doesn't maintain an upgrade waitlist. It would be nice if you could set up an EF alert, but I don't think this is possible. Also note that the call center hours are limited for BA's US office and you have to call within those hours and you may have to wait on hold as long as 30-60 minutes to reach a BA operator unless you have elite status on BA (AA elite status doesn't count when calling BA). You can only call the US BA call center if your Avios account is registered in the US. Also note that the UK BA call center is open longer hours and they are 5 hours ahead of US EST. So although you may see an upgrade seat open up on your TATL flight, by the time the US BA call center opens up for you to call, the seats may be all gone as the UK/EU passengers already called their respective call centers to upgrade before those in the US can call in. So upgrading from BA PE to CW is a good use of Avios points, but it can take a lot of legwork as well.

I have missed many BA upgrades due to the above. Also BA will depart with empty seats in CW, even though there are people wanting to upgrade from PE with Avios. They don't have to release upgrade seats (aka award seats) and often times will depart with many CW seats open. This is different from AA where if a J seat is available and someone wants to use a SWU or miles+copay, they will allow you to upgrade at the gate. BA will sell you the empty CW seat at the gate if you want to pay the full ticket price difference between PE and CW and the re-ticketing fee.