Well, IMO, it depends on the headphones. Don't take my words for truth (I'm not responsible for you following my advice) but those look like pretty rugged headphones, and I wouldn't worry about it. Lets see, the power handling is 100mW on those. I guess you probably just wouldn't want to put a hugely loud powerful source through those. In summary: Poor quality sound will not damage it, unless it is turned up very loud, in which case any music quality would damage it. Bass boost will probably not damage it, unless it it turned up very loud. Altogether, just use common sense. Don't turn it up too loud.