In this case you can try to use PulseAudio loopback module which will redirect audio stream from your input device to the default output device. Please run the following command on the server and then verify audio on the client side:
pactl load-module module-loopback source=alsa_input.usb-Burr-Brown_from_TI_USB_Audio_CODEC-00.analog-stereo
This loaded loopback will be also visible in pavucontrol (Playback and Recording tab).