Assuming that (a) you're following your procedure consistently, and (b) the deck was properly shuffled to begin with, it doesn't make a difference.
What your move-to-back procedure achieves is nothing more or less than what you could achieve by drawing the tiles in the ordinary order but filling up the spots on the game board(?) in a different, but fixed order. You could figure out exactly what the different order would be by starting with a stack of cards numbered 1 to 14 (in that order!) and deal them onto the board using the move-to-back order. The exact sequence you'd find is not important, but it is important that the initial position of a tile in the deck completely determines where on the board it will end up -- no matter which of the ways to deal you use.
Now, the assumption that the deck is properly shuffled to begin means that each of the $14!$ ways the deck could have been arranged is equally likely (for simplicity we're assuming that there's some way to tell "identical" tiles apart, even though this difference may have no gameplay effect). This again means that each of the $14!$ ways the tiles can end up on the board are equally likely.
However, the move-to-back dealing achieves exactly the same thing! Each of the $14!$ possible ways the tiles can end up on the board corresponds to one and only one way the deck must have been arranged before the move-to-back dealing started. And since each of those were assumed to be equally likely, each resulting distribution is also equally likely.
You would need a more involved argument than this if you're accused on choosing on the fly how to continue your deal based on which tiles you have already placed. A more careful analysis would still vindicate you (because each tile you see will reduce the number of possible configurations of the rest of the deck in such a symmetric way that you cannot get any information-theoretic advantage from it), but it would be rather less accessible.
And if the tiles were imperfectly shuffled to begin with, your procedure probably cannot make it worse -- unless the imperfection of the initial shuffling was of a very specific sort, fine-tuned to be made worse by your procedure.