Nevermind the fact that some of us actually are engineers by trade, but both Dale and myself have extensive headphone experience. The Sennheiser HD600/650 are a very well known quantity to me, having owned many iterations of it over the years and paired it with many different amps both simple and exotic. The Massdrop HD6xx is a very very close variant of the HD650, so I can say with a high degree of confidence that it is going to sound best with an amp.
Dale is correct that the Sennheisers experience a large impedance swing in the midbass. If your headamp has a larger output impedance, this is going to cause a shift in the frequency response. As well, it may potentially cause a sag in the power delivery which may lead to distortion or clipping. Issues of damping factor may also result, although the audibility of this is generally very small.
That all said, the HD6## family are still good headphones even if you don't have a proper amp, which is why I said he should get it and worry about the amp later.
