While RadeonSI Gallium3D has OpenGL 3.3 support in mainline Mesa Git, the R600g driver that supports from Radeon HD 2000 through HD 6000 series GPUs does not. R600g right now officially only supports OpenGL 3.1 but there's been out-of-tree work towards OpenGL 3.3 compliance with this older open-source AMD Linux driver.
As the first work to hopefully be merged soon, David Airlie has proposed the R600g Geometry Shaders support. OpenGL GS is a requirement for supporting OpenGL 3.2 and is one of the major blockers in the path to OpenGL 3.3 support.
David wrote on the Mesa mailing list, "This series adds support for geometry shaders to r600g for evergreen and later GPUs. I don't think r600/r700 support is that hard, but I haven't had time to look at it at all, and I expect possible erratum. This passes most of the piglit tests on my BARTS board and doesn't hang the GPU anymore than normal piglit does."
Implementing Geometry Shaders for the Radeon HD 5000 amd 6000 series is spread across 25 patches to Mesa. The patches can be found via this Mesa-dev mailing list thread.