No.
radiation damage is actually only a little direct damage to the cell: it is mostly the cell recognizing some minor damage and then killing itself in a process called apoptosis
This is done far, far sooner than the damage usually has any impact because of the danger that damaged DNA poses: cancer.
Cells will happily kill themselves if they can save their host from cancer.
So any resistance to radiation will mostly involve reduncancies and processes that make sure that a cell can take more damage before it terminates, not direct radiation hardening. An improved resistance to cancer is a positive side effect.
If your organism evolved in a environment where actual radiation hardening is needed they woudn't evolve at all because that place would be sterile.
see for example Deinococcus radiodurans, the most radiation resistant organism on earth. That tough cookie just has tightly coiled and multi-copied DNA.