If Aliens do invade earth, chances are they will do it for our natural resources (and they may well count humans as a natural resource just like how we view cattle). Apparently earth has way (around 1,000 times) more gold than it should. Scientists are suggesting meteorites delivered the gold, and if so, I dare say not every planet would be so fortunate.
If gold is valuable to us, imagine how much more valuable it will be to a race that has 1,000 times less of it than we do.
As for how long it will take for nations to band together, well I think that will depend entirely on how aggressive the Aliens are. If they just attacked a single country and came up with some half plausible reason for it, chances are a lot of the other nations will dither and not get involved until it became obvious that the Alien's aim goes beyond that single country and that we are all equally at risk.
If an Alien power is advanced enough to get to us, you would assume that they are clever enough to come up with such basic PR tricks. Assuming of course, they feel it is worth the effort to try and fool us and pick us off one at a time.