It's a common theme in movies regarding alien invasions (or even peaceful arrivals) that upon contact, Earth will put away its domestic squabbles and unite as one.
Usually it's done by humanity rebuilding itself after an alien invasion wipes out a great deal of Earth's governments, people and infrastructures - basically eradicating "borders" of countries in a way. Forgetting the scifi horrors, I think it's safe to assume that any intelligent, civilized extraterrestrial life that contacts or reaches Earth will be fairly peaceful in reality.
So, if aliens make contact with Earth either by landing or other means, would Earth unite itself?
I think not. Or at the very least, not at first. If mankind has the ability to simply "unite" itself out of the blue, it would have done so already. There are too many cultural, economic and political conflicts across the entire globe to simply drop at the appearance of an out of this world people. If the extraterrestrials are peaceful like I'm assuming, Earth may grow to unite itself but it'll be years - maybe decades - before we truly become "one people" among the stars.