I did this with my "end of evil " disc. if you look at the purple clouds at the bottom, I used some reds on the back of the disc.
In your scenario you will get a shade of blue green on the top and bluish close to the same on the bottom, but it will look strange. If you dye out by the wing you will see more of a color separation, murky yellow on top blue on bottom.
Yellow has high transparency as does Orange and red. Blues, purples and browns more opaque and override the prior colors even if on the underside of the disc.
your colors will never soak into the disk so far they will mix.
velocity discs does a lot of clear plastic as well, he probably has a more experience than I do