Yes we would unite because it gives us a common foe. For the first time, we could partition the world into an ingroup/outgroup, where the ingroup contains the entirety of humanity. That has never before happened in Earth's history, but it's not an extraordinary step to take. People form communities form small towns form citystates form coalitions form countries. We're already well past the limit on how many individual relations a human brain can form (~150) and we seem to be chugging along fine, so there doesn't seem to be an upper limit as to how large a human society can get.
http://en.wikipedia.org/wiki/Robbers...ave_Experiment
To lessen friction and promote unity between the Rattlers and Eagles, Sherif devised and introduced tasks that required cooperation between the two groups. These tasks are referred to in the study as superordinate goals. A superordinate goal is a desire, challenge, predicament or peril that both parties in a conflict need to get resolved, and that neither party can resolve alone. Challenges set up by the Sherifs included a water shortage problem, a "broken down" camp truck that needed enough "man" power to be pulled back to camp, and finding a movie to show. These and other necessary collaborations caused hostile behavior to subside. The groups bonded to the point that, by the end of the experiment, the boys unanimously insisted they all ride back home on the same bus.[3]