I have a very similar setup with the NAD C372 integrated and Sennheiser HD580s. The impedance mismatch is even worse with the integrated (220 ohm output impedance, if I'm remembering right) to the 300 ohm impedance of my Senns. But the combination sounds surprisingly good. I also considered buying a headphone amp (and owned a nice tube headphone amp in the past) but have been very satisfied with the NAD's performance for as often as I use headphones. Like me, you could always leave a headphone amp as a future option and enjoy what you have meanwhile--a pretty happy medium!
One note if you haven't absolutely decided on headphones yet: I used to own the Senn HD555/595 (prior models to the current HD598) and they are not as neutral or highly resolving as the HD580/600/650. Also, with the NAD my HD555/595 had grainy treble and huge mid-bass bump that my HD580 does not have--the HD580/600/650 is a much better match.
That said, the HD580/600/650 are a class above the lower Senn lines, and if you need to keep the headphone budget down you can pick up the HD580 for ~$130 used and the HD600 for ~$220. The HD580 and 600 have the same drivers; I've owned both and am very happy with the 580 now. Hope this helps.
Check this out, too, and search Head-Fi for NAD and Sennheiser:
http://www.head-fi.org/t/471769/will-headphone-jack-from-nad-integrated-power-hd600