OS X Server bound to Active Directory, but OS X Clients who are logged in as AD users prompted for username when connecting to OS X server file shares
Ok, to answer my own question, it appears that if the Mac client uses AFP to connect to the MAC OS X Server, then it will not use AD.

If I instead browse the the Mac OS X server using SMB  (eg, connect to: smb://servername )  - then it will connect as an AD user (with no prompting for username/password) and will list all the shares that AD users have access to.