Yes they do. AMD even provides the specification up to the HD4000 series at the moment.
Take a look here at AMD's R700 instruction set reference guide.
There is also an open source project called Nouveau that does reverse engineering of the Nvidia instruction sets.
Note that Nvidia has a slightly different architecture than AMD because they do not use VLIW but scalar execution (although multiple threads are additionally grouped in what is called a Warp or a Wavefront).
Also, not every OpenGL/Direct3D call maps to a "GPU instruction". For example, when binding a texture the driver will only set appropriate hardware registers that tell the GPU which texture memory to use for sampling.
Real programs are only run when executing shaders or stream processing kernels on the GPU.