Does the primer color make a difference

Here's an example... Start with a black plastic part and try to change it to red or dark blue with SEMS dye. Wont happen easily. Take the same black part and dye it with SEMs light gray for blue, beige for red. You'll get nice coverage with less paint, and the correct shade.
I found it interesting that all OEM plastic parts in late model Fords were cast in a neutral beige, and they could use the parts without dye and call it camel/beige interior.
Another example... I chemically strip gauge needles for repaint. The orange comes off and the white primer remains. If the needle has been bent, a piece of the white primer jumps off so I have to remove all the primer. New orange paint over white primer will be just a little brighter than new orange over bare aluminum.
This is with a florescent water base acrylic, the SEMs dye is lacquer based, so what type paint probably doesn't matter.