| TL;DR yes and no (thanks to DSPs, technically some were an integral part of the GPU): In the era of semi-programmable graphics pipelines, of which there was the N64, PS2 and GameCube, you would not be able to solve general-purpose problems using only that pipeline: given a handful of colour mixing formulas, registers, textures and vertices to control the pixels to write back to memory, I fail to come up with any tangible problem you could hack them into solving. However, what the 3D generation of video game consoles had to bundle with the hardware in order to process complex scenes at interactive frame rates were digital signal processors (DSPs). Think of them as regular processors, but with an extra vector unit, allowing you to crunch enormous amounts of data in parallel (single instruction, multiple data instructions, or SIMD).
This was essential to perform geometry transformations, which benefit greatly from parallelism, in order to build graphics commands to pass down to the rasteriser. I am unsure if the SEGA Saturn and PS1's vector-accelerated instructions are sufficiently general-purpose to allow them perform any computation you wish to do, but at least starting with the Nintendo 64, you could write microcode to accelerate any task you'd like, provided you were brave enough to deal with the harsh memory constraints of microcode and obscure documentation. To give concrete examples, the PS1 came with a dedicated chip (the MDEC, or motion decoder) to decode MPEG video frames from the CD directly into the VRAM to display on screen. While the N64 doesn't have dedicated video decoding chips, its signal processor was designed in such a way to allow microcode to do an equivalent job (not to mention YUV texture decoding on the rasteriser's side). So this did not stop a talented Resident Evil 2 developer fresh out of school to write an MPEG video decoder microcode to be able to cram two CDs worth of video data (around 1 gigabyte, down to a 64 megabyte cartridge), of course with other smart decisions like data deduplication and further compression/interlacing. Another one was Rare developers writing an MP3 audio decoder microcode to store large amounts of dialogue. And finally, in recent times, a developer managed to write an H.264 video decoder microcode, for a machine that was released almost a decade prior to this codec's birth. You can also accelerate physics and anything else that would benefit from SIMD, really, and in fact, while more modern CPUs integrate SIMD instructions in their tool chest that compilers can take advantage of, the PS3's Cell processor was a brief throwback to the old hardcore ways, before GPGPU became king. You could almost treat the DSPs as the compute units of modern GPU architectures: they definitely processed the vertices, and nothing stops you from adding a "vertex shader" pass, however, because it's not directly integrated into the graphics pipeline, it's harder to emulate a true pixel shader, you might be limited to full-screen pixel shading since there's no feedback from the rasteriser about which pixels exactly get written to memory. |
Actually, you could probably just use the depth buffer as write-only with constant values to identify objects as different kinds, and use a "pixel shader" pass to apply effects on those annotated pixels, but I assume this might be a pretty expensive technique.
... Now that I think about it, it's not unlike modern rendering engines.