In a war between Humanity and the Supernatural, Humanity won't actually stand a chance. That 700 million number is astoundingly optimistic, and implies that Humanity itself would be united. Not a chance. You'd see various nations dusting off old scores to take advantage of the new chaos.
Anyway, the point is that we're fractured beyond any hope of cohesion. It wouldn't be the Supernatural World vs. 700 Million, it'd be the Supernatural World vs. 4 Million, vs. 2 Million, vs. 9 Million, vs. 1 Million, etc. In a large-scale conflict, you'd see nations seal up their borders and leave most to fend for themselves. Old alliances, like Europe and the US, might stand, but most of the rest of the world would be too focused dealing with their own issues to present any kind of united front. Especially because borders and troop movements simple don't matter to most of the supernatural world. They can take a force of several thousand, destroy a high value target, then disappear, only to reappear a day later on the opposite side of the planet. It would be a war of hopeless defense, because it's not like many of these supernatural nations have a place on earth for the vanillas to take. Most of vanilla conflicts have been about seizing or defending territory, and it simply won't work against an enemy that doesn't have any.
Vanillas can develop countermeasures and eliminate threats as they crop up, but they can only do that if A) they know where to go, and B) they can get there in time to fight. Just scaling it down to the US, you're talking about having to watch and defend every inch of, what, 3.5 million square miles? With the current US population size, you're talking about drafting, arming, and supporting a relatively small number of capable infantry. The best asset the US military would have would be air superiority. Gunships may not be good enough in a guerrilla-style war with so much land to cover. They could surely respond faster than ground troops, but you're talking about crucial minutes to get in the air and get to the fight. Bombers won't have much to bomb. They could hit places like Chichen Itza, sure, but that doesn't help much if you're fighting a force based in the Nevernever. And imagine the havoc a couple of rogue wizards could have on complex, computer-driven machinery, like jets. All it would take would be a few of them to go to the Supernatural side to turn it into a ground war.
Anyway, my point is that in battles, humanity has a real shot. We're really good at killing things. If ten thousand Fae assaulted a major city, they'd be dealt with within hours, days at most. Someone would figure out that they don't like iron, and you'd have countermeasures developed in short order. If a Black Court scourge sprang up in Manhattan, and someone noticed, it'd be eliminated immediately. Someone would figure out how to deploy holy water as a gas grenade or something, and the problem would go away. But in a full-scale war? There wouldn't be any pitched battles; there wouldn't even be urban-style street-by-street combat like we saw in Afghanistan. It'd be strike after unpredictable strike, and we'd lose, badly, without supernatural allies to counter their advantages.
I do think it's likely that the Supernatural side of things would be just as fractured. To Groinkick's point, I don't think it's likely that gods would side with the supernatural; they'd be guarding the resources that keep them and their mantles juiced up. I think the White Council would pitch in on the side of humanity, for the most part. I think that many of the individual groups would have their own rivalries and competing interests.
Now, a specialized group, like the proposed Watchers, is a different story. If, for example, they decided to eliminate the White Court, provided they had sufficient numbers and intelligence, I don't see any reason they couldn't pull it off. You're talking about what is, in my understanding, a supernatural intelligence agency. If they have significant resources, access to funding, maybe mercenaries, and their own agents (assassins, for instance), then a coordinated, decapitating strike against the White Court could eliminate them, for all intents and purposes. They may not have the reach to get all of them, but they can neuter them by reducing their ranks, seizing their assets, freezing their accounts, et cetera.