Do you think humans would recover?

The smarter humans would have begun backward engineering of the alien technology and used it to conquer the whining sniveling humans... it would all be a question of where the smarter humans came from as to which country would then rule the world.

That's a good question. Same with like Walking Dead or other apocalyptic visions of future planetary catastrophe. I think it might be a good thing because when you consider that we have so far not needed space aliens or zombie-making microbes to destroy our world .... we're actually doing a pretty good job of it ourselves ... incidentally, as has almost every past human society that ever existed on Earth.

The book "Collapse" by Jared Diamond takes historic collapse of civilization and goes into what happened to them, and the biggest factor is the leadership class who want things to keep going status quo and ignores problems or will not respond to them because they are insulated by their high status and privilege. Like for example Global Warming, or I like to say Planetary Hotboxing, or even this COVID-19 pandemic, the people in charge think it will not affect them and so they dump all the risks and danger on everyone else.

So, if that cycle of out of control technology was stopped by a Martian, or in this case alien invasion and we were able to survive it and even win ... we might have a whole new series of myths and legends about what worry about and avoid in the future and bring people up with a difference consciousness?

Stephen Baxter wrote The Massacre of Mankind which is an alternative history covering the aftermath of the first invasion. It was particularly interesting because one of the things I failed to appreciate about the original book is that only Britain was invaded. So in Baxter's history Prussian Germany becomes the dominant power in Europe whilst the USA just trundles along quite happily.
Apart from Britain and it's Empire taking a bit of a pounding everyone else is ok and happily continue on - until the second, world wide, larger scale and better prepared attack.