As far as I know, there are no differences between the Early Access code (now full game on Steam) and Limited Edition code, both give the same game. So there not really a point in redeeming the code that comes with the Limited Edition.
The extras in the Limited Edition (dlc for example) will normally come as a different code that you'll be able to add to your game.
Not entirely sure about this though, just pieced together the info that's spread across there forums, the steam forums and kickstarter.