Arrington didn't really lose the job to Shipp; he had 22 touches to Shipp's 23 in 2006. (Ayanbadejo was actually #2 on the team with 26 touches). Basically, Arizona didn't give the ball to backup RBs in 2006; Shipp happened to get the ball at the goal line three times against the Rams (the #31 run defense) so his fantasy stats looked better.
I think it is likely that the #2 RB in Arizona will get more touches in 2007 than any of them did in 2006, and I think Arrington is more likely than Shipp to be that RB. That means his value is non-zero, though it's still pretty low; upside is Kevin Faulk unless Edge gets hurt.