Is you take "uncureable sickness" as a mutation, then yes. But not mutation in the way you were suggesting (http://www.bmoviecomic.com/?cid=73).
Regardless, what point would that have?
Radioactivity is not dangerus in low dosages and if treated properly. Also its makes creatures crippled from birth, meaning that a child born from a heavly-dosed mother will be very weak. If you can get photos from the Hirosima and Nagasaki victims, you'll be very clear what I am talking about.
Also the first link talks about a wolf-dog crossbread, not "mutation" (though it is mutation in a certain way, but lets not go there). The second it talks merely about how people from Chernobyl are effected by the leaked radioactivity, not dealing about radioactive damage itself (to be a bit more specific, it deals about the LACK of dealing with the radioactive damage).
Radioactivity is very nasty, but it couases terrible death, not miracles.
And for mutation: there are several types of mutations, most which are not good. "Controled" mutation either by genetic engineering or trough netural selection is "good" (we are talking about relative terms here). Mutation caused by envarioment, such as radioactivity damages the body, often in a way that the body cannot repair itself.