No, ionizing radiation is only harmful to an organism as a whole when its amount gets too high. We are constantly bombarded with very small amounts of ionizing radiation that occur naturally, and we get along just fine with our lives without being seriously harmed by this radiation. There are trace amounts of naturally-occurring radioactive atoms in the air, in the rocks, in our food, and inside our bodies. When these atoms radioactively decay, they emit ionizing radiation. By its nature of being ionizing, such radiation can damage individual molecules, even at low intensity. But if the amount of ionizing radiation exposure is very low, our bodies can handle a few damaged molecules without any problem, so that there is no net harm done to our bodies.