The dyes in Diablo have interesting cosmetic effects. Do they have any sort of gameplay advantage? Or are they purely decorative?
Vanishing dye + PvP? Maybe?
Otherwise, no. Dyes change the color of your armor but that is the limits of their power. For the aesthetically inclined it helps them stay color coordinated but they provide no practical benefit other than being one further outlet for achievements.
Achievements related to dyes: