There was never a time they weren't turing complete (e.g. you could always just run the same NAND shader iteratively on the same pixel buffer and compute whatever you like using pixels as binary storage) but once GPUs moved away from fixed pipelines it became easier to do whatever you wanted with them. Nowadays there are also compute type shaders which are kind of what you are talking about, running little functions on the GPU with no intention of actually shading anything with it or even working with graphical entities for that matter.