So I recently thought it might be worth it to try and dither the textures while converting to RGB565 before C2 does it. Here are the results:
First in the native 640x480 resolution: Then in 1920x1080 via nGlide: The door and rear bumper are good spots to check for the differences. While it's ok in low resolution (the banding on the door seems to disappear), there's already obvious patterns in the textures. This problem becomes very annoying in high resolution.
The two problems are 1) the pattern used for diffusing pixels in my test, 2) C2 textures being way too small anyway and making the pattern very apparent.
I've used Telegraphics 5_6_5 Photoshop filter, via IrfanView because I don't have a 32-bit version of Photoshop installed

Then I could give it another try, also upscaling the textures with an AI.
[edit]
Installed PS7 so I can use DepthDither, much better plugin.