Not a bad idea, but due to the way Minecraft works, it's not the most practical solution.
Just a little bit of technical detail - Minecraft has a 16 character limit on most of the strings in the protocol, such as player names, inventory names, etc. Each color code takes 2 characters. This would mean that for a normal player, their name would be cut off by 2 characters if it was 16 characters (as The Arena Master made the example, his name would appear as The_Arena_Mast); an admin's name would be cut off by 4 characters due to the color code of bold as well (so Bic's name would appear as Bicentennial); and a developer's name would require 4 extra color code characters per character, 2 for each color of the rainbow and 2 for each bold (meaning, for example, my name would appear simply as "Fo").