If the armor dye would work in the same way as Void Edge illusion, the base color of the armor you dye still matters. Void Edge covers your weapon in void dark blue color (which matches perfectly our current void form btw), but you can still see base color of the item. I expect that armor dye to work the same. You basicly combine two colors. Now I imagine priest Antorus tier with void edge modification, it would be glorious.
What I would like is to have option to change color of the glowings. I really like old Sunwell tiers, but I hate that fel radiation coming from the shoulders. It certainly works for some Tmogs, but I'd like to change them for some others, fel green does not mix with ren'dorei blue-purple-gold color scheme pretty well. I also think future high elvish ren'dorei would appreciate that too.
Unfortunately, it can't. You have to farm visions.