Oh I don't know about that, the entire battle has their fingerprints all over it. I doubt many, if any, participated in the actual fighting.
But stirring up factions that haven't been at war in thousands of years, beings acting outside their normal behaviours and ignoring protocols and treaties...it's classic Black Council. Not to mention, Ethniu got Balor's eye somehow. She was locked in a tower by her father when he lost the Eye to her son. Now it's possible Lugh (her son) returned it to her, but then who ripped out her eye for her to place Balor's Eye in? My guess is a Walker of the Outside. Who else could damage her so? Also, how did she get Titanic Bronze? Only the Hekatonheires (Hundred-Handed Ones) knew it's secrets, even the Svartalves were not sure of it. Lots of questions and no answers.
An angry being like her was strong enough, but someone (or a group of someones) armed and armoured her and pointed her at her ancient foes. And why? To weaken their defence of the Outer Gates.
Also, consider that the Black Council (or rather, Nemesis) was behind the assassination attempt of Etri. This was done to destabilise the already fragile relations between the Accords members (this is said in Battle Ground). It's quite clear that after the Red Court failed to destroy the White Council, the Black Council unleased another force against them. I am sure there is more.
Further, the presence of Drakul would also hint at Black Council involvement. Whether he is aligned with them or not, I suspect he is connected to them, either as possible occasional allies or competition.
The Whamps and Svartalves working together was about pure survival. Had they refused, Mab (not to mention the other Accord members) might have made them pay later. More importantly though, failure to stop Ethniu would have likely meant their destruction (at least locally, and probably totally in the mid to long term).
The Battle wasn't merely to tire out Harry. That merely was one of Nemesis' many options. As Nemesis itself says, it's not so much a plan as an act of faith. I see Nemesis as more like the Joker than Bane, if that makes sense. An agent of chaos. Everything it does it merely to create more chaos, conditions that suit it and the Outsiders, that ultimately weaken the barriers that keep them out. It's all about the Outer Gates, and to a lesser (but still important degree), the prison at Demonreach. Remember, the Outer Gates came under major assault JUST as Ethniu announced her impending assault on Chicago.
To the Outsiders, what is a small dust-up like the Battle of Chicago but a bit of distraction to the forces allied against them? The Outsiders are fighting a multi-verse scale war, even one universe is ultimately a very, very tiny part of it all. Even if Harry's universe is very important, perhaps more important to the greater battle than most universes. The Outsiders might number in the trillions, likely very nearly infinite.