You could, but why add more connectors to the mix? If you have not already found that your headphones sound the way you prefer, then perhaps it is just the headphone. No amount of break-in will "fix" a headphone. Break-in may alter the sound signature a tad in that it often reduces sibilance in the high end, but rarely if at all will it magically make the headphone sound better. That all comes down to taste and it may just be possible you prefer a different sound signature.
Why types of music do you listen to most? What gear do you use the most to listen to said music?