No, per the USAT regulations, listening to music is not permitted while competing.
Article IV, Section 9:
Participants may not use communication devices of any type, including but not limited to cell phones, smart watches, and two-way radios, in any distractive manner during the competition. A “distractive manner” includes but is not limited to making or receiving phone calls, sending or receiving text messages, playing music, using social media, taking photographs or using in a oneor two-way radio communication. Using any communication device in this manner during the competition will result in disqualification