It could have been A or B. I think he could have given the Sox a chance at either. One player doesn't make a bad team a great team, but the 2009 Sox were a very good team. When we speculate about how Halladay would have changed the Red Sox season, we can't assume that that everything else would have stayed static. I'm not saying that his presence would improve the teams' offense, but his presence could have affected games beyond those that he pitched.
His ability to go deep into games could have helped give the bullpen a shot in the arm at a time when it was running on fumes. I don't think it is a huge stretch to think Halladay could have won three games against the Yankees in the second half. That by itself would put the Sox 2 games back of the Yankees. I don't think its a stretch to think that Halladay or a more refreshed Pen could have picked up an additional couple or 3 games the rest of the way.
If we didn't have enough to catch the Yankees, it's not a stretch to think that Halladay could have won game 3 against the Angels. Who knows what happens in game 4 at Fenway and game 5 with Lester and Beckett on the hill in those games. I think you would have to give the Sox a shot.
Schilling used to talk about how the execution or 4 or 5 pitches in the course of 120 pitches usually was the difference between winning and losing. It doesn't take a lot to change the dynamic of a game to account for the difference between a win and a loss. Similarly, with a playoff team, it's not hard for me to believe that the presence of Halladay could have made a difference to the Red Sox season.