Actually not that well. Most (cheap) plastic hair combs are made with 2 molds and those leave a small sharp edge on the gap. Thus, the comb will very likely have a sharp edge, even if you don't feel it well with your fingers. And that sharp edge goes for both scratching the screen as well as damaging the hair as every pin of the comb has 2 sharp edges.

For people with longer hair, those sharp edges on typical plastic hair combs do really make a huge difference. I wouldn't try one of those as a emergency stylus. Of course if you smooth out the sharp edges thoroughly before using it as emergency stylus, sure.