Connection, sure. But not MOTIVATION.
His intent to kill all the "Green Aberrations" and the motivation behind it are -clearly- outlined. Sylvanas and the treatment of Undercity are almost an afterthought compared to that. Yeah, he was disgusted by the undead. But not -nearly- so disgusted as he was with Thrall. And it wasn't what lead to his ultimate decision in destroying Thrall's "Kingdom of Murderers and Thieves" rather than "Torturers and Necromancers" or "Gravediggers and Corpses" or some other phrasing.
I'm not saying he wasn't angry, horrified, upset, whatever about the corpses and the experiments. I'm saying that people are putting WAY TOO MUCH emphasis on those things compared to what the character is actually -actively- communicating.
As to WoW-Wiki, I wouldn't put -too- much faith in their phrasing since it's written by players, not developers. Each with their own personal takes and biases on the events of the story. But it -is- worth noting that Varian intended to go to war -before- leaving for the Undercity.
Full disclosure: I joined WoW when Cata Launched (My mother finally convinced me to get an account). So I didn't get to -do- the Battle for the Undercity event. I only read about it and watched videos of it on Youtube and the like.
Apparently Varian initially thought the Horde had betrayed the Alliance at the Wrathgate (Which is dumb, since the Horde lost just as many soldiers and heroes, there, as the Alliance, but there's a reason Varian was a Warrior and not a Mage...) and intended to go to Undercity to conquer it. Then Jaina told him the truth of what happened and he changed is plans, slightly, to "Kill Apothecary Putress, -then- Conquer Lordaeron"
Soooo... we're actually arguing over something largely irrelevant, since what happened in the Undercity is largely irrelevant: Varian had decided to kill Thrall and take Lordaeron before he ever left Stormwind..?