Air quality on Earth would go down a bit, but there would still be air. Food supplies would be chaotic, but some crops somewhere should survive. As for severe temperature swings on a post-apocalyptic Earth, they'd probably still be easier to handle than what NASA calculates on Mars as nightly lows of -128 C.
I realize that colonizing far away places is what Earthlings do. (Columbus, Cecil Rhodes, etc.) But the lets-go-to-Mars crowd strikes me as an extreme manifestation of Dunning-Kruger