I've experimented with this and the results seem to vary depending on the headphones. I have a set of planar magnetic hifimans that don't have enough sub-bass out of the box, but can easily make tons of sub-bass with eq adjustments. On the other hand, some of the other headphones I tried this on sound like they're just distorting more when I try to apply similar levels of eq compensation.

There's also no way to apply a system wide eq to an iPhone, so you'll need an external device.