Nah, whether the sun blew up, imploded, or turned off like a light and disappears. The inhabitants of earth would perish soon after. If the sun blows up, we are flashed cooked just before the explosion strips the earth of its atmosphere and crust.
If the sun implodes or disappears, we loose not only our heat source, but also the gravity well. Earthquakes would be the least of our worries as we were sling shotted out of the solar system or were compressed along with the earth into something the size of a grain of dust and sucked into the resulting black hole. Hypothetically ofcourse