The answer is no.
A dimmer is a device that is originally created to control the
brightness of lamps. This is done by altering the total power
delivered to the lamp and thus the brightness.
To clarify the question, do fluctuations in the amplitude (power) of the electromagnetic waves produced from a light source cause cancer?
lumec.com reports a study in specific to unnatural light patterns on the human body:
Where it becomes an even more important concern is that it has been
known for over a hundred years that cell division inside the body
follows a circadian rhythm, we have just explained that the circadian
rhythm is affected by light, and we also know that damage to cell
division is characteristic of cancer. You do the math…
Studies have shown that mice, when exposed to unnatural patterns of
artificial light, developed certain problems related to their cell
division and also to the transcription of many genes. In other words,
they were in for some major health problems on the long run, if they
remained exposed to that type of light – and so would we.
As well as an article from The Daily Star:
Blask and his colleagues have been recognized for research on the
cancer-stimulatory effects of light at night through the suppression
of melatonin, a key hormone, according to a Bassett Healthcare media
release. A study in 2005 by Blask and his colleagues provided evidence
that light at night promotes growth of human breast cancer. The study
also provided insight into why breast cancer is increasing rapidly in
developing countries and industrialized societies.
It seems that evidence is leaning heavily toward the fact that either A) our natural cycles rely on light at specific times, or B) the lack of production of melatonin in the brain has adverse and sometimes cancerous effects.
The information provided against artificial light is almost strictly based on non-direct processes in the body - not the amount of energy produced by the light source.
Our bodies are constantly subjected to all different areas of the electromagnetic spectrum and radiation:
For comparison, the average 'background' dose of natural radiation
received by a person per day, based on 2000 UNSCEAR estimate, makes
BRET 6.6 μSv (660 μrem). However local exposures vary, with the yearly
average in the US being around 3.6 mSv (360 mrem)
To clarify one point, light is essentially radiation as being part of the electromagnetic spectrum. This consists of radio waves, micro waves, wireless devices, visible light, x-rays, etc. If varying the voltage that goes through a light bulb has anything to do with cancer, every human on Earth would have cancer after being exposed to huge amounts of every type of wavelength known and unknown to man every day.