Ultimately the way this plays out is that the aliens would fail to accomplish their objectives. If the aliens are savvy, they’d never even consider adopting such a plan.
This is because of the fundamental imperatives of geopolitics. Geopolitics is a very simple idea on the face of it, but produces immensely complicated behavior. It is simply stated as such: Everybody identifies with and works for the people closer to them than they do with people farther from them. What drives people is geographical closeness.
The concepts of nations, states, and countries fall out of this idea. People band together to form communities, which are then organized into polities. Close to the top of the hierarchy are countries, and entities like the European Union.
A state is not a nation, is not a country. A state is a governing institution, whereas a nation is the people that are being governed. “Country” refers to both at once.
States used to be weak, and still are in many developing world nations, but these days are quite robust. The primary geopolitical imperative for people is survival. Modern nation-states have achieved this, very little is capable of bringing down a national government.
How they achieved this is very interesting. If you look at a country like the United States, just about everything that could bring down the government is planned for and secured against. A recent example of this is the Presidential Inauguration, perhaps the most-secured event in modern times. Millions are sunk into performing this one ceremony.
All of this relies on nationalism. Nationalism is the belief people have in their country. At the end of the day, America is an idea, and that idea is defended by Americans. If somebody acts in a truly un-American fashion, Americans are going to take up the defense of the nation themselves. Ditto for French, British, German, Japanese, and so on.
We have plans for any conceivable contingency, but we also have Americans, the last line of defense for the Constitution. This defense-in-depth strategy, ending with you and your neighbor dusting off your pea-shooters and charging the invaders, is what provides a modern country with its security. They are pretty much invulnerable to anything except another country destroying their military, occupying their lands, and pacifying the population. Everything else is the realm of fiction, not reality.
It is this depth that would-be alien conquerors would run into if they tried such a stunt. You see, we went through the problem of rogue leadership all the way back in Roman times. Humans have figured out how to contain this sort of thing. Any leader is only as good as the people that do his bidding. If those people refuse, then the leader has no power. You see this in the current virtual mutiny of public officials leaking Trump’s plans to the press.
When organizations are found to have differing goals, divisions shift along loyalty grounds. This is just geopolitics in the small. When survival is not at stake, then we identify and work with those who share our economic best interests. Also personal connections play a role. This can be abstracted over as loyalty. So the part of the organization that is loyal to the aliens will fight over control over the organization with the part that is loyal to America.
Since one of these factions has the entire nation at its back, and the other doesn’t, the aliens will get found and kicked out in short order. An ‘alien McCarthy’ will show up and name and shame the invaders, their careers will be ruined, and there won’t be enough effective organizational energy left for the aliens to achieve any goals.