What carrier are you on?  I have a Tmo Note3 and with the NF9 version of Android, I got full native USB audio.  While I'm using a custom rom, I confirmed the developer did not do anything to the audio.    http://forum.xda-developers.com/note-3-tmobile/help/usb-audio-usb-audio-player-pro-t2807427

T-Mobile Galaxy Note 3 working natively using the Tweaked 3.8 rom and iFi iDSD Nano!   I tested YouTube, default music player, PowerAmp and one video game, Another World. All worked!! I used the Effortless Guide to install stock NF9, but instead of TWRP 2.8.0.0, I used 2.7.2.0. At the point...