In my experience, the need for an amp is often overstated: I've got a Sennheisr HD600 and a Beyer DT880 (250 Ohm) and both sound fine straight out of a portable player with no additional amping. I'm sure amping them improves the sound a bit, but it's not essential to enjoying them.
However, the K601, when I had it, was one of two headphones that I felt *did* sound quite a bit better when amped (the other was a DT880 600 Ohm).
It wasn't totally terrible un-amped, and some music sounded fine, but listening to recordings with a wide dynamic range didn't sound great - the bass would distort or sound 'farty' and the highs would sound 'wrong'. When I plugged them in to my little FiiO portable amp, or the headphone out of my hifi separates amp, they sounded better.