I would say: possibly, though the difference may not be enormous. There are two factors as I see it: 1) cleaner amplification if you need more power (though it sounds like maybe power's not an issue), 2) is the DAC in the iPod good enough for a better amp to matter, assuming you're not also looking for an outboard DAC?
I think it depends on just how much you want to squeeze out of the system. I had K701s for a while, and I could definitely tell the difference between different amp sources - e.g. headphone jack on my receiver at the time vs. a dedicated (tube) headphone amp (but of course there you're throwing ss vs tube into the mix). But it's sort of like receiver vs. separates with speakers, there's a difference but it's not night and day. Just depends on how particular you are, whether it's worth it. If you're listening in a quiet room, it'll be more worthwhile IMHO than if you're using it on a bus or train where it's noisy anyway (and the K701s block no external noise).
It is entirely possible that adding a decent headphone will help the sound, moreso with open style headphones than the super-efficient IEM style. Of course, the perceived improvement will be limited by the encoding format you use for the music. I cannot fathom attempting by to improve the sound of files encoded at any lossy rate below 192kbps, and even then I wouldn't bother with it unless the audio were at 256kbps or higher.
All music files are in Apple lossless. As for the quality of the dac I am limited to the ipod's internal dac. I can't afford a device that pulls a digital signal from an ipod, and even if I could I don't currently own a digital pre-amp or receiver, so I would need an external dac as well.