"It might be possible for a guy like Appel to file a lawsuit, since he's not a part of the players union (yet), but if he does so, he may be alienating the players as a whole.
I would also think it possible/likely that Pittsburgh could file a complaint against MLB for instituting the slotting system that screwed them out of their pick, especially after they demonstrated last year that they are now willing to pay big money for amateur bonuses."
Since other pro sports leagues and unions have negotiated limits for incoming players and never been sued, I don't see as he'd have a case.
Pittsburgh would be suing themselves since they were a party in the union negotiations. The MLB negotiates with the union on behalf of all teams.
Pittsburgh knew all the rules going in, but chose to draft a hard to sign player. They took a risk and they lost. Had there not been signability issues, he would have gone higher in the draft.