depends on how big it is and what it is made of and how fast it hits
if an object the size of the moon struck the earth traveling at half the speed of light, i think all life, human and cockroaches etc , would be gone
I think if the Moon simply collided with Earth, period, everything would die, except for microbial life I'd imagine.
The immediate impact would likely send such insane ripples through all of the tectonic plates that they'd just shatter. The molten material from the impact site would spew into space and probably rain down everywhere (molten rain - now that's exciting).
Take those effects and just keep 'em coming over a long time, magma probably spewing up everywhere due to the shattered plates... If we knew that was happening, I'd probably book a one way flight to wherever scientists thought the impact site was and just get shit over with.
Even if people can live, I really don't want to make with the primal living and living in an inhospitable environment for the rest of my life, even if that only ends up being a few weeks.
How cool would it be to stare up at the sky and see the moon fill the entire scene as it came crashing down? Instant, plus probably the most awesome thing to be the very last thing you see before making yourself the meat of an Earth-Moon sandwich.
In all likelihood, if there was any object approaching Earth that all of the scientists agreed would be a world-ender, I'd probably do the same thing. Go to the predicted impact site, and just camp out for a week. Also, would bring a smorgasbord of drugs.
That's just absolutely necessary. Meet instant death on the highest flight of your life.
That, or I'd camp somewhere outside of the immediate impact zone, but close enough that I'd only get a handful of seconds before the blast reaches, that way I could at least witness the actual crash and see the blast coming.
This is assuming I've seen the evidence scientists are using to proclaim we're all dead, and my limited knowledge of crazy smart science can't find any obvious holes in their we're all dead theory.