Does GPU usage affect video quality?

Yes, it does.
It all depends on the GPU used and how the manufacturer uses it in conjunction with the sensor. When the GPU is activated, digital stabilization can be turned off, the strength of the noise reduction effect can change, and the color space can change. The GPU is always processing and modifying the signal, even if the signal is just passing through the GPU.
Turning on the GPU allows you to adjust various settings that affect the signal, which are not available without it. While dimming is available without a GPU, things like chroma and discoloration of highlights and shadows are not. Saturation, shadow and highlight adjustments can also work differently. The GPU provides many possibilities for obtaining the finished image. But it also takes away features like 10-bit recording.