Can you beat StarCraft 2's Brutal difficulty without building a single unit?

In this challenge run of StarCraft II: Wings of Liberty, we ask and answer one simple question: Can you beat the game on the highest "Brutal" difficulty without creating a single new unit?

StarCraft II: Wings of Liberty is a 2010 science fiction real-time strategy video game by Blizzard Entertainment. It is a sequel to the 1998 StarCraft and the Brood War expansion pack, and was followed by the Heart of the Swarm and Legacy of the Void expansions. It follows the story of rebel Jim Raynor on his mission to confront Kerrigan, the Queen of Blades and leader of the Zerg swarm.

Missions:
0:00 Liberation Day
2:06 The Outlaws
7:01 Zero Hour
12:39 Smash and Grab
23:58 The Devil's Playground
27:16 Welcome to the Jungle
30:44 The Great Train Robbery
39:03 Cutthroat
46:29 Ghost of a Chance
50:37 Engine of Destruction
1:05:30 The Dig
1:15:07 Whispers of Doom
1:20:15 A Sinister Turn
1:25:18 Echoes of the Future
1:27:15 The Moebius Factor
1:31:37 Supernova
1:38:15 Maw of the Void
1:44:25 Gates of Heal
1:50:35 Belly of the Beast
1:57:26 All In