In short no. Balanced TRS outputs are mono signals, so sticking your headphones in the aux won't give signal in both ears. AUX outputs are not designed to have headphones plugged in directly to the jack.
However! You can connect an AUX output to a Headphone Amplifier, like the Presonus HP4/HP6. These units have a Mono switch that will take a mono signal that only comes out the left channel, and put it in both ears. Very cool feature that isn't in a lot of other brands.
https://www.presonus.com/news/articles/balanced-unbalanced