I've had a player go to five arbs, because I (unintentionally) dragged out his service time... he spent one and a half seasons in the minors after one and a half in the bigs. (He was a failed first-round pick.) Now, he also had 99 Patience... even after five arbs he would still have taken the LT. Which is to say, he never declared he wanted to walk.
I just can't see how this would work. You have a player whose contract is up, but if you bury him in AAA and leave him on the 40, then wouldn't his contract automatically roll over at 65k or something like that? There's gotta be something about a post-arb player that his arb years invalidate that.