The water itself? no. But radioactive particles can still get mixed up in it. Also, the Simpsons have done a terrible job at making people think spent nuclear material is stored in oil barrels and glows green. This is what nuclear waste ACTUALLY looks like.
Ver archivo adjunto 8247747
The water actually DOES block most nuclear radiation, to include Alpha, Beta and Neutron. It can also attenuate Gamma and X-Ray Radiation. But spent fuel rods don't really put out much of those provided they are kept cool. Which incidentally water is also very good at doing. Eventually the spent fuel completes its half life cycles and stops putting out hard gamma's and won't melt into slag if exposed to air. Its still dangerous, but at this point its sealed into a lead and concrete sarcophagus that looks like this.
Ver archivo adjunto 8247761
The plan at this point is to then bury these sarcophagi under a mountain in Nevada, but Harry Reid killed that idea. But only after taking all the money to build the facility. Cock sucker.
With respect to jumping into a retaining pool with spent fuel rods in it...you...can. But its not recommended. Not because the water itself is radioactive, but because you could accidentally breath in some particles suspended in it that broke off from the fuel rods. And that is...not a good thing.