No, Poser doesn't use the advanced Quadro features. While Poser does have hardware shading since version 6 or 7, it's not particularly advanced and any gaming card since then can display what Poser can do for hardware shading.
For that matter, Poser's hardware shading isn't really that good. Many of the "SSS" shaders just glow in hardware shading mode and don't look even remotely like the rendered result, and anything with a trans map simply doesn't show up.
I don't know what version of the OpenGL shading language Poser uses, but I would be surprised if it's anything more recent than OpenGL 2.0.
If you look at some of the most recent Autodesk products such as Mudbox, Maya, 3ds Max and Softimage, you can see some really good examples of what a consumer level (gaming) graphics card can do, with the realtime shadows and normal and displacement maps, bumps, reflections, shaders, OpenGL photometric IES lights... and all that good stuff.
And then there's 3DCoat with its CUDA and voxels.
Poser actually is a really poor example of what can be done with OpenGL, aside from its very fast redraw speed with large textures. Everything else in Poser, OpenGL-wise is.... lacking.

Yeah, the qauadro cards are used more for CAD programs where they can display wireframe models with full anti-aliasing much faster, as well as some more architectural-specific shaders, but a quadro has little or no advantage in a "typical" 3D application over a regular high quality gaming card.