On the hair that is previously colored, you will not likely see any change at all. But the 'virgin' hair that is your regrowth will take on an auburn shade if you do an all over color and then they'll look different from the ends.
If you want more of an auburn look all over, you'd be better off lightening some sections (just to the orangey stage) and then applying an auburn 'toner' over top. (semi-permanent/no-ammonia color works best as a toner) Make sure you color your regrowth the dark brown color first though so that your hair lightens from roots to ends evenly.