Depends on the scale of the atomic annihilation. I mean, it might be possible to detonate enough nukes to make any sort of life impossible. But you’d need a lot of nukes, and the conditions on Earth would have to be very extreme. So I think it would still be highly unlikely you could kill all life on Earth, as we know of many weird forms of life that life in strange places.
In which case, life would survive, evolve and adapt to live on the new conditions on Earth. So yes, it is possible 🙂