To use Touch ID a local account is required on the system. In order to use Touch ID with QAS AD users, the user needs to be a mobile account. This allows the user to have a local user record.
To enable an AD user as a Mobile Account, do the following:
1 - Login as the AD user in question
2 - Open up System Preferences
3 - Click on Users & Groups
4 - As an Administrator, unlock the lock icon on the bottom left
5 - Where it says "Mobile Account:" click on "Create..."
6 - Adjust settings as required, then click "Create"
7 - Click "Create" again
8 - OS X will then ask you to enter the password for the AD user
9 - To configure Touch ID for use with a Mobile Account, enable the user as you would a local user.
For more information setting up a mobile account please see this article from Apple.