We suggested this in another forum (because Esoteric uses a custom driver for their USB implementation and does not currently support Linux as an OS for the USB driver).
http://forum.audiogon.com/cgi-bin/fr.pl?ddgtl&1354751988&openmine&zzDoggiehowser&4&5#Doggiehowser
Here's someone who bypassed the USB input on a K-03 with a Bel Canto REFLink. I gather the USB implementation on the K-01 and K-03 are the same so the gains on your system may be similar.
However, I did also mention that the Aurender was designed primarily as an AES output device so that (and SPDIF) may be a better bet.
The alternative would be to trade in your Aurender for the newly announced model that has a clock input. That would provide clock control from an external device (like Esoteric's) that can sync the data transfer between the Aurender and the K-01.