In all protested games, the decision of the League President shall be final.
Even if it is held that the protested decision violated the rules, no replay of the game will be ordered unless in the opinion of the League President the violation adversely affected the protesting team’s chances of winning the game.
If the league does determine there was a detrimental effect, the game could be restarted from the point of the infraction. Considering that the Yankees were sitting on a five run lead at the time, there's a good chance that they could lock down the victory if given a second chance.
It's pretty clear that Sox pitching coach John Farrell signaled to the bullpen before telling the umpire that Beckett was hurt. Girardi isn't disputing whether the injury was valid, just that the call was made before the umpire was informed of the injury.
There is a ton of subjectivity involved here. How will the league interpret the word "adversely"? Delcarmen getting as much time as he needed to warm up obviously wasn't the reason that the Red Sox were able to come back, but it definitely helped them stop the bleeding to some extent. Getting to face a guy who was only allowed to throw eight warm up pitches would certainly have been an advantage for the Yankees, particularly if Francona chose to temporarily insert a position player instead. So by a strict definition, it did "adversely affect" their chances of winning the game, however infinitesimally.
Although it doesn't say it in the rule book, I'm guessing the commissioner will have the latitude to determine degrees of adversity. In other words, was the advantage the Yankees lost enough to warrant restarting the game from that point? Will Bud Selig take into account that the Yankees were winning by five runs at the time? Will he note that the Sox came all the way back and won by just one run? It's a logistical mess to restart the game and you'd have to assume that the league would lean towards avoiding it if the decision is close.
Bud Selig works in mysterious ways, but unfortunately, I'm pretty sure this one isn't going to get overturned.