Radon is a noble gas. It's not going to affect fiber or wiring... but yes, if you're going to spend much time down there, definitely a good idea to check for it.
Interseting - I have high radon (mitigeted in the house via a fan), if I burry fibre what will I need to do to get something that will work? I have an outbuilding that I want to give internet.
Well technically a nuclear bomb would also degrade the jacket of fiber cabling pretty badly, but we don't really concern ourselves with that since it means you're dead and the house is gone anyways.