Digital EQ is far cleaner in terms of distortion and phasing than analog EQ. By the way, human hearing is rather insensitive to phase unless it's really pushed to produce an effect.

In fact, EQ, as well as other DSP, is applied in all active headphone and speaker implementations to produce performance characteristics that many passive counterparts would struggle to achieve by electro-mechanical means.

We've even got a database of EQ settings, maintained by a professional acoustic engineer, for thousands of different headphones, earphones and IEMs designed to put them into compliance with a very well researched, industry standard, target frequency response curve:

AutoEQ is a project for equalizing headphone frequency responses automatically, and it achieves this by parsing frequency response measurements and producing equalization settings which correct the headphone to a neutral sound. This project currently has over 4000 headphones covered in the results folder.

Can a headphone be overdriven by EQ into audibly distorting? Of course, it can. However, if it is under the circumstances that we're concerned with, which is correcting to a target, then its got quality control issues to begin with and is a poorly designed product I'd avoid purchasing.