This depends on your definition of "mostly disappear". If you mean, ignoring, soundstage, imaging, distortion, and other parameters that affect sound, then yes, but even a non-audiophile could easily discern the difference between an open-back vs. a closed-back headphone with identical magnitude response (by your definition, the differences between these two headphones should have mostly disappeared).
From linear signal analysis, magnitude adjustments do not provide enough degrees of freedom (and thus are not sufficient) to transform any response into another response. And this is true for practical sound signals not just theoretical concoctions.
Take a look at any headphone review at rtings.com where they try to capture other parameters in addition to magnitude response. They test for phase response (related to imaging), PRTF (pinna-related transfer function --- related to soundstage), and harmonic distortion. These would not automatically match between headphones that were modified by gain adjustments to have identical magnitude response.