Maybe, depends on where you live. There would be a few survivors, but the climate shift would destroy large-scale agriculture and, therefore, civilization.
DID YOU KNOW THAT IF THE MOON WAS GONE THEN WE WOULD ALL DIE? THIS IS BECAUSE THE MOON STABILIZES EARTH'S AXIS. IF IT WAS UNSTABLE, ONE HALF OF THE WORLD WOULD BURN AND THE OTHER WOULD FREEZE.