I make no assumptions to the nature of this planet. There are high chances it does not have an atmosphere or a lithosphere. But in a planet that shows a high level of radioactive activity, would it be advisable to probe for life, or is it improbable? Either way, why? How would we go about detecting life in such planets?
At what level do you define life ? Bacterias, sentient, instinctive inteligence ?
For example, they can withstand temperatures from just above absolute zero to well above the boiling point of water (100 °C), pressures about six times greater than those found in the deepest ocean trenches, ionizing radiation at doses hundreds of times higher than the lethal dose for a human, and the vacuum of outer space. They can go without food or water for more than 10 years, drying out to the point where they are 3% or less water, only to rehydrate, forage, and reproduce.
Roaches are also known to be able to live in radiation but it does not fill the requirement to be without atmosphere.
Earth-like life would be run into problems if enough energy is delivered through radiation, so that the organisms can't handle it. As bacteria are known to tap into unusual energy sources for earth-life, I think it should be thinkable that some alien life form can utilize the radiation as energy source for life (as plants utilize the sunlight). There might be still another limit: if radiation start to destroy the structural integrity of the molecules too fast for repairing, this would be deadly for every life-form.
Generally spoken simple life-form can withstand higher radiation-doses than humans, because of simpler genetic information, so we could expect more simple life forms in high radiation.
If we're talking about more advanced/complex life, I would think that a protective layer would be all that's really needed. The evolution of life is a fairly complex and uncertain subject. As one example, on earth it took some 2 billion years for the first plant to appear on land. It can be a very slow process it seems, as well as, at times, a very fast process.
If there was a planet with very high radiation, I think all it would take to protect the DNA for reproduction and have not overly-mutated offspring would be a refillable sack of water around the entire body - not too different than how we have skin and fat as protection. An outer skin of water around the entire body would protect from a lot of radiation. Water is pretty good at blocking radiation.
Now, whether such an evolutionary adaptation like that is likely, I have no idea but I see no reason why it wouldn't be possible. Certainly sea life would have a chance even in a high radiation environment.