I don't know about overprinting per se, but you can already use whatever foreground+background colors you want; how much benefit would overprinting be?
That doesn't solve the two-colors-per-cell challenge. But it makes for some very realistic terminal images.
For higher fidelity rendering, I think the next best option is supporting image protocols like sixels or Kitty inline raster images. I'm not sure how overprinting would compare to existing options.