My suspicion, and I've been wrong...is that they will pursue this legal fight up until the time that a court tells them they must arbitrate under USADA rules (unless somehow they win a court battle before that, which would surprise me). When it reaches the time where they must arbitrate or accept the penalty, my suspicion is that they'll decry the "unjust nature of the process" that "stomps on Constitutional rights," and walk away - still claiming to be clean and still claiming that the process simply wouldn't give them an opportunity to demonstrate that. And an ever-shrinking segment of the population will believe that.
A couple months later, a new triathlon series will be announced with Livestrong as a primary sponsor...