yes, its a thing. I replace my carbon on a 2yr cycle to avoid any issues. The amount of radioactivity will depend on the amount of radon being captured in your carbon. I suppose its possible to estimate the radioactivity if you know your radon level but those chemistry calculations were beyond my comprehension.
Understand that not all radioacitivty is created equal. Generally in radioactive decay chains, there are alpha, beta, and gamma particles given off. If you look at the three remaining naturally occuring decay chains, (I'm ignoring the 4th that doesn't include radon and is currently sitting at Bismuth 209 with a half life of billions of years) radon is typically giving off an alpha particle but degrades into other radioactive elements that can give off beta and alpha particles. Alpha particles are high mass so they can be blocked by very little (like clothing or your skin) but beta particles are lower mass and can penetrate greater. Because of their mass, alpha particles are more dangerous. Because of their ability to penetrate, beta particles are probably more likely to cause a problem. However, all this assumes both are kept outside of your body. When ingested, the alpha particle would be more dangerous but you don't want either inside of your body. And with water being used around the house, there is a tendency for the radioactivity to collect (cleaning clothes, washing dishes, showers, brushing teeth, etc.). All this to say that something like a geiger counter doesn't differentiate between the type of radiation (alpha, beta, gamma) but just that radiation is present. So its not that a geiger counter won't help distinghish if your GAC filter has a higher level of radiation then say outside in the open air but that the type of radiation also matters. None of this is simple so I made my solution simple - replace the GAC often.