Radiation can affect living tissue in two ways:
Irradiated: is when the tissue has ben subjected to radiation, but not in direct contact with radioactive material (e.g. when undergoing radiotherapy). In this case, the damage uses to be in the DNA/RNA, and, as it's already done, dampeners wil have no effect.
Contaminated: when the tissue is in direct contact with irradiating material (e.g. nuclear fallout) that keeps irradiating it. In this case, the damage already done would not be haled, but the dampeners will help to stop new damges until it is eliminated (if absorbed) or claned. Unfortunately, if absorved, most of those materials are toxic, aside from radioactive, and that will be unaffected by dampeners.
Where dampeners could be helful is in radiotherapy treatments, dad could be quite more precise (if dampeners are).