I built a machine that dual-boots between Windows Server 2003 R2 and Windows Server 2008 R2 (both x64, installed on the same RAID array).
Is it possible and/or advisable to run the Server 2003 installation directly off the physical partition in Hyper-V?
No, it's not possible to do that. It would make a lot more sense to use the disk2vhd tool from SysInternals and make a VHD out of the Server 2003 installation. Then you can boot it within Hyper-V.
This begs a question, though. What are your OSes currently set up to do? Hyper-V was designed to be the only thing that runs physically on a machine. While you can install other server roles simultaneously, it's not recommended that you do that.
Presumably your Server 2008 was doing something useful for you. If you want to continue doing whatever it was that you were doing in that OS, before you turned on Hyper-V, you'll now want to do that in a different VM.