Yes they do... however it does somewhat depend on how the flight number is done and your ticket set up.
If you're flying codeshare, you'll have to call AS and ask for your record locator so that you can look the flight up on their system. Make sure your DL number is in there and it should recognize you as elite and show you as on the upgrade list.

You may get upgraded over 24hrs from the flight, or not until you check in... if it goes past that then its unlikely to clear at the gate.