> If the energy isn't enough to ionize, then what is there to study?
DNA is conductive, and there are researchers who believe that this might be an important component in how the cell detects and repairs damage to its DNA [1].
There have been a couple of papers that claim that DNA can act as a fractal antenna allowing it to react to wavelengths that you would at first expect to be way too large to affect it. Here's one [2], which claims it interacts over a wide range of frequencies with a resonance at 34 GHz.
If DNA charge transport does turn out to play an important role in how the cell identifies damaged DNA, and if it turns out that those fractal antenna claims are true, then we'd have a potential mechanism for non-ionizing, non-heating radiation to increase cancer rates.
Note that it would not cause cancer, but it might prevent a cell from finding and repairing damage that if left unrepaired will lead to cancer.
The first part of the above, that DNA is conductive, is firmly established. How the cell detects damaged DNA is not known. That charge transport plays a role in that is currently just one theory that researchers are studying, but it is a theory that if it turns out to be true will not surprise anyone.
I haven't been able to find much on fractal antennas, especially very small ones, so can't tell if the claims about DNA acting as an antenna have merit.
[1] http://www.its.caltech.edu/~jkbgrp/Research.htm
[2] https://link.springer.com/chapter/10.1007/978-981-10-5699-4_...