If you look at the definitions in army_icons.txt alonside the icons in army_icons.dds, you can see that the first 14 icons are the generic vanilla ones, which have a neutral color and have the implied default color_override = yes. These 14 army shields are colored automatically by the game, or the user can select another color in the color picker. The remaining icons are all DLC-locked and have their own colors as stored in the texture file, which the game or the user can't change.
Therefore, color_override = no means that the game renders the icon as is from the texture file, it doesn't paint it with another color.
Since this attribute can only be found in army_icons.txt, we can't determine if it's handled globally by the game in any icon definition, or if it's limited only to handling army shields, army group shields and naval equipment roles. You'll have to experiment by yourself to find that out.
