Take it from a transfusion director, Odell is completely correct. Red cells (RBCs) can also be frozen (which kills any remaining white cells) after being glycerolized -- this is something the military has been doing for years. The only problem with frozen cells is their short shelf life after thaw or they would be used much more. But this also kills the non-RBC cellular elements.

Red cells, the foundation of most transfusions (there can be platelet and WBC and other specialty infusions, but most transfusions are to make up lost blood volume where only the red cells matter) have no nucleus -- they are just tiny bags of hemoglobin which is the molecule that carries oxygen. To prevent reactions in the recipients (beyond the ABO/Rh/minor antibody reactions for which blood is "typed and cross-matched") WBCs and other cellular components are close to eliminated in preparation. Irradiation would take out anything left, but WBC numbers are so low in packed red cells that it likely does not matter anyway -- the recipient is pretty good at taking out foreign white cells that are transfused.

So take transfusion worries off your "really worried about this" list -- there are more serious things about which to worry. Just make sure you get packed red cells, which is almost certainly what you would be getting anyway if bleeding out.