I don't expect anything to happen. Perhaps the fact he was called up, thee, day after the deadline goes in his favor. But in these things, if it opens the flood gates for other players to grieve, I doubt they rule in Bryant's favor.
I am in favor of any rule change that starts service time from signing day, not from call up to the bigs day. It's not fair for the fans who have to sit through what the Orioles are doing, not promoting their future stars. It's not fair to guys like Trey Mancini who won't be a free agent until he is 31.
Messersmith would have opened the floodgates as well, yet an arbitrator still ruled in his favor.
Personally I think the two sides will agree to some sort of settlement--maybe the Cubs give Bryant a two-year extension that would pay considerably more than if he went to arbitration his final two years eligible. I agree that it would be a thorny precedent should there be a ruling in Bryant's favor--particularly since the CBA doesn't specifically address the issue--but at the same time, there's always the risk that an arbitrator could be sympathetic to Bryant.
Such a ruling would certainly impact strategic planning around baseball, and would also change how teams make promotion decisions. Those types of issues are typically not something you want to put at the mercy of an independent arbitrator.