I had a little luck getting an upgrade while flying on AASaver award ticket on US Airways (post-merger, non-codeshare).

When I tried to check in online, it presented me an option to purchase an upgrade for $215. I didn't want to spend that much for a 2 hour flight. When I arrived at the airport, I simply asked the checkin agent if there is a seat available in First. To my surprise, even without asking a question, he upgraded me right then and gave me a new boarding pass.

Not sure if its allowed, but I was happy for the upgrade!