Exponentially better than it does with Guilliman alone, since he wouldn't have to do everything himself.
Vulkan would be the sane, level-headed, pillar of support that the Imperium relies on, all the way up to Guilliman. You'd probably see a slight lessening of the grimdark meat-grinding given his outlook and opinions.
Corax is the problem. He's doing better as he currently is, tracking Lorgar's bitch ass in preparation for another beatdown once he inevitably catches up.
Really, what you want is the Khan, possibly the Lion, over Corax. Significantly better tactical acumen and outlooks for the current state of the Imperium.