Its been said here a few times that with some discipline and the exercise of proper board visualization (examining the board consistently for threats, checks, and captures), that 1600+ may well be attainable by doing that and that alone.
That said, if you combine that with any of the other methods of self-improvement available to you, you will progress faster and farther. As you get higher up the rating scale, board visualization and discipline alone are just not enough anymore. Though its certainly a good place to start. You can know all about the finer points of chess strategy: good vs bad Bs, N outposts, strong squares and colour complexes, isolated d pawns, hanging pawns, pawn nails, and on and on... but if you routinely hang pieces or drop them to simple tactical shots, all that knowledge won't help you much. But it will once your board visualization ability catches up and you learn to focus.