Blue dye is put into some de-icers to let you know where you have applied it. Will it stain the paving bricks? The answer is -- maybe.
As long as the dye stays on the surface, the sunlight will quickly break it down and it will lose its blue colour. If you have quality paving stones (which are denser than lower quality ones), and they have been properly sealed, then the dye will not stain the bricks. However, if you have no sealant, or a very porous paving stone, then yes, the dye will probably stain.