Single person, no.
Gradually evolve resistance as a species? Possibly, if we were exposed to it enough. We’ve already evolved some resistance to the most common damaging radiation we experience – melanin to protect from sunlight.
The trouble with radiation is that it literally tears molecules apart. One big problem there being when the molecules in question are the DNA in our cells.
Bacteria and viruses can be fought off with molecules/proteins etc. our bodies produce. Radiation would need to be stopped from entering the body, or be absorbed by something that won’t cause us harm if it is destroyed by radiation.
As far as evolution goes, suddenly developing a radiation absorbing slime layer might reduce your chances of having offspring more than skin cancer in your 70s would.
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