Even then, once the threat is gone, we'd go right back to being terrible to each other. I mean, we "unified" against the Nazis in WW2. But then black Americans and black veterans went right back to being treated like garbage as soon as the war was over. Don't see why something like this would be any different.
If anything, they'd continue to rationalize it by just assuming the groups they already hate are in cahoots with the aliens and feeding them information, and then never admitting that they were wrong (y'know, again bringing up WW2, internment camp style, just like how we locked up Japanese-Americans for assuming they were feeding info to Japan simply because of their heritage. Also see: stuff like the Hollywood Ten under McCarthyism/Red Scare, again assuming people are traitors though that time based on political ideology rather than nationality).
Unfortunately, the worst of us seem quite good at developing ways to continue to hate each other, no matter the situation, so I just can't see how even a scenario like that would be enough, to be honest. =/