My experience has been that arb-eligible players will still arb, even if they are in the minors and off the 40. I have, however, gotten pleasant surprises (lower than expected demands) recently on arbing players in the minors, although they were relatively low in overall rating.
Another advantage in sending an injured player to the minors is that his ML service time stops increasing. If his ML time is under the "rounding threshhold" (156 days?), you may get another arb at his previous experience level.