The Radiation Center is meant for protection from ICBM missiles/nukes. These are not needed until after the 60 minute mark, due to the fact that nukes can not be created until then. If your base is large, make sure you have enough radiation centers to cover your whole base!
This building will reduce the damage of the ICBM Missile by half, and yes, radiation centers do stack (i.e. having two radiation centers reduces the damage to a quarter of the original damage).