Can normal algos run on PyOpenGL?
Is PyOpenGL the answer?

No. At least not in the way you expect it. If your GPU does support OpenGL-4.3 you could use Compute Shaders in OpenGL, but those are not written in Python

but simply run a "vanilla" python script ported to the GPU.

That's not how GPU computing works. You have to write the shaders of computation kernels in a special language. Either OpenCL or OpenGL Compute Shaders or, specific to NVIDIA, in CUDA.
Python would then just deliver the framework for getting the GPU computation running.
I want to write an algorithm that would benefit from the GPU's superior hashing capability over the CPU.
Is PyOpenGL the answer? I don't want to use drawing tools, but simply run a "vanilla" python script ported to the GPU.
I have an ATI/AMD GPU if that means anything.