It depends on what your source is. If you will be plugging it into the headphone out of a receiver or standard desktop CD player (those tend to have the larger 1/4" connector like the K701), you are set for now. While their headphone section is an afterthought and will not be quite as good as a dedicated headphone amp, it should still be sufficient. You really need the amp if you are using a low-power source like an iPod or a laptop computer's headphone out (those usually have the smaller 3.5mm connector).
One misconception is that amplification is primarily about volume. Sure, an amp can usually drive headphones at higher volumes, but the primary advantage is control. When your amp sends current into the headphones to move the magnetic coils, there is an action/reaction effect and the headphones send an opposite current back. A solid amp will shrug off that current, a weak one will not and the sound will not be as tightly controlled as it should, among other things the frequency response will not be as crisp and the phones will sound dull. This is known as the amplifier's damping factor, primarily related to the amp's output impedance, unfortunately few amp manufacturers quote their products' damping factor.
Many people on Head-Fi are afflicted with upgraditis, and if you wait long enough you will find a decent amp up for sale at a reasonable price. I myself use a Musical Fidelity XCan V3 with my K701, but there are many others available (specially from China) at lower prices. You should still expect to spend at least 50% of your headphones' price on amplification (once again, if you don't already have a headphone out on your receiver or CD player).