The short answer as to whether these new GPUs work on the open-source driver is: yes. To some surprise, when booting to the latest Linux 2.6.39 Git, Mesa 7.11-devel Git, and the latest xf86-video-ati DDX Git with this brand new graphics card, kernel mode-setting had worked and even Compiz desktop compositing. The PCI IDs for the Turks are already in there and it was working.
However, when launching OpenArena, Nexuiz, or any of the other OpenGL games with the Gallium3D driver, we quickly ran into problems. Like what happens when running the Radeon HD 6870 on the open-source driver, each OpenGL game eventually has a hard lock-up. It's been happening with the Radeon HD 6870 for quite some time and the Radeon HD 6570 shares this same problem.
So using the very latest open-source AMD Linux driver code will work for kernel mode-setting and compositing, but running any OpenGL games will eventually fail. As such, there are no open-source Radeon HD 6000 series benchmarks to deliver at this time. For now such graphics card owners will need to learn to live with the Catalyst driver exclusively (and hope that the Radeon HD 8000 series is magical).