Would the Chicago Cub Sox Be A Playoff Contender?

None of the projection systems like the chances of the Cubs or White Sox to compete this season. Things look so bleak for each team that it's hard to even trick yourself into thinking the best case scenario includes fringe contention.

So, while watching Comcast SportsNet's SportsCentral, I started thinking: Could Chicago combine the two rosters and end up with a contender?

I used Steamer projections for the Cubs and White Sox to come up with this roster. I took the highest-ranked player at each position, with their WAR projection. We'll use the DH because this offense is going to need all the help it can get:

C: Welington Castillo (1.9)
1B: Anthony Rizzo (3.8)
2B: Darwin Barney (1.2)
SS: Alexei Ramirez (1.9)
3B: Luis Valbuena (1.4)
LF: Alejandro De Aza (1.1)
CF: Adam Eaton (1.8)
RF: Ryan Sweeney (1.1)
DH: Jose Abreu (3.5)
Bench: Tyler Flowers (0.8), Justin Ruggiano (0.9), Marcus Semien (0.7), Starlin Castro (1.9)

Thoughts: Even combined, this offense scares no one. To have only two players project for over 2 WAR is just sad. The prime suspect is an outfiled that still looks like a pile of spare parts. To be sort of fair, the outfield projections are dragged down a touch by platoon projections limiting at-bats. But still. Jeez.

SP1: Chris Sale (4.2)
SP2: Jeff Samardzija (2.8)
SP3: Jose Quintana (2.5)
SP4: Edwin Jackson (1.7)
SP5: Jason Hammel (1.5)
BP1: Travis Wood (0.7 --- really??)
BP2: Nate Jones (0.9)
BP3: Matt Lindstrom (0.4)
BP4: Pedro Strop (0.4)
BP5: Jose Veras (0.3)
BP6: Scott Downs (0.3)
BP7: Ronald Belisario (0.3)

Thoughts: Steamer took a steamer on Travis Wood, but I kept him as the "long reliever." The rest of the bullpen is full of primary bullpen guys. This looks like a perfectly useful pitching staff, with a "true ace" out front.

In total, the roster is split as evenly as can be: 13 Cubs and 12 White Sox.

I'm thinking this roster would be a wild card contender in either league, particularly if we can trade for a boost in the outfield at the trade deadline.

Granted, you might advocate for different roster selections, but what do you think? Are the Cub Sox a contender?