12 pitchers is already overkill with a decent 4-man rotation in a postseason series. Assuming Darvish did come back and pitch well and so did Morrow the Cubs would certainly have the depth to carry 13 pitchers (and no, Chatwood not among them) if they wanted. But that doesn't mean they should.
The "decent 4-man rotation" is the issue. As it the assumption that Darvish will come back and pitch well.
To me, the reality is that the Cubs do NOT have a decent 4-man rotation. Hamels, after 9 days of rest following 10 days for his previous start, still took ~100 pitches to get through 5. Lester and Hendricks nibble a lot and normally are at or over 100 pitches within 5 innings. Even before his injury, it was exceptional for Darvish to finish 5 innings; and several of the games where Maddon did try to push him beyond four innings, it wasn't so much to win the game as for long-term-season reasons, to protect the pen, or to build Darvish up, or to get him a W, or to build his confidence, or something. Coming back after the injury, I don't think you want to be expecting Darvish to be giving you 5-inning starts.
Sure, if things go right, some of the starters might be sharp and well-rested and give a five or even a six-inning start in the playoffs. But for the most part, I think in the playoffs you want to be ready and willing to be pulling starters pretty early, if they aren't unusually sharp. Hope for 5 innings, but be willing to settle for 4 or 3 or even less. No point in letting Hendricks or Lester or Q or Darvish pitch tired or pitch "off" in the playoffs.