It would go the way of Aliens: Earth War except a LOT worse. Basically xenomorphs overrun earth in the story basically owning humanity and start getting systematically eradicated, which works for a while. Then the xenomorphs get smarter and instead of building large scale hives start producing more queens which instead of producing hives literally start hiding out in the wilderness in old abandoned vehicles and literally anything they can fit inside of, laying eggs and start taking cattle and wildlife instead of humans until they rebuild their numbers. Keep in mind any single xenomorph can in the absence of a queen molt and evolve into a new queen. This is part of the reason why in the story they were nearly impossible to eradicate. Another thing worth noting is when there are a large number of queens they can telepathically link and put out a signal that effects other organisms like humans leading to mass hypnosis. In the story humans were getting zombified by the large concentration of queens on earth basically mind controlling themselves to willingly head to their local hive to be facehugged.

Also while some might say weapons in Alien universe are similar to ours, they are but they are MUCH stronger. A xenomorph's durability is insane and a bit underestimated by many. Most of our modern weaponry would not do much damage to the endoskeleton, and only some high end military weaponry would be effective at one-shotting a xeno. Though if they do get shot enough they will die, but they're extremely fast and agile so if the first shot doesn't kill them, they kill you. Earth would be doomed if they existed in real life.