Yes, the very point & end goal of atomic chess is to explode the opponent's king.
Think of it this way: in [regular] chess, the goal is to checkmate the opponent because the king will be "captured" in the next move. This is why it is impossible to check (and therefore threaten capturing within a move) the opponent without providing guaranteed safety to your own king in that move -- since the king who falls first will ultimately lose.
Exploding the opponent's king while in check is like capturing in regular chess - and besides, how can your own king be in danger when the opponent is without a king to command its pieces? They have already lost the game/battle/war and will surrender.