How loud would you have to listen to hear audible distortion in low frequencies?
This is difficult to answer because it would depend on the level of distortion in the lower frequencies to begin with. And also how much you're raising the bass levels relative to the rest of the frequency spectrum, among other things. Some dynamic headphones may have enough distortion in the bass or lower frequencies that they will sound rather loose, or woolly, or muddy in the bass right out of the box, with no EQ at all!
I don't think Amir has done a review or measurements of the HD 660S yet. (I can't find them anyway.) But here are a few THD plots from
his review of the HD 650. The first shows the THD at three different sound pressure levels. This is with no EQ btw...
The 2nd image shows the THD levels before and after the bass was boosted with EQ, measured at the same sound pressure level...
Whether THD is the best way of assessing these characteristics in a perceptual sense is still very much open to debate. So one should take the above info with a little grain of salt. If distortion is higher in the bass to begin with though, then it's only likely to become worse (and more audible) if that area is being boosted compared to the rest of the frequency range.
In my experience if you use negative preamp correctly to avoid digital clipping, then there is no problem to boost bass in software EQ with decent headphones. In case of 660S I cannot raise volume high enough to distort before worrying about my hearing. But that's with EDM where whole spectrum is very busy so that might mask sound of distortion.
Clipping would be a different (but also important) type of distortion than what's described above. I think you're absolutely correct to be using a preamp with negative gain to avoid that though, if you're using other EQ filters to boost
any portion of the frequency range.... be it bass or otherwise. I understand that most users of open-back headphone will probably be trying to do their boosting in the lower frequencies though, to compensate for the more rolled off response there.
Open headphones (especially dynamic driver headphones) generally have a much harder time achieving good volume levels in the lower frequencies of the bass because they just can't maintain the same level of pressure in their cups as a closed back headphone can. And their drivers may often be deliberately tuned or pushed close to the brink of audible distortion in order just to deliver a rudimentary level of response in the bass frequencies. So that's why I think you need to be a little bit more cautious with how much boosting you do in those lower frequencies with open dynamic headphones.
You probably do not need to be as cautious with open planar magnetics though, because they are often better extended in the lower frequencies to begin with. And may have lower or more uniform distortion in the lower frequencies than some dynamic headphones do.