Everyone says so, but in reality the more likely answer is no - the greenest thing you can do in areas where regulatory constraints limit electrical power generation and delivery is to use more of it.
Notice that this isn't about about dollar costs -everyone knows that using less costs less - but about whether reducing your power requirements produces cleaner air, cleaner water, or cleaner land.
Notice too that the obvious correlations don't work: energy use and pollution are inversely, not directly, correlated: the richest areas of the world use the most energy per capita, and are the cleanest - while the poorest areas are both dirtiest and the most energy starved.
The history of green politics isn't conducive to faith in public or media opinion either. It was media support for green activism against nuclear power that led to today's petrochemical dependencies and thus the CO2 those same greens now hold responsible for the putative horrors of global warming. Ethanol, a current political favorite, is considerably dirtier than gasoline, and the green's favorite alternate source: wind power, is probably the dirtiest of all - most wind generators never break even on the energy that goes into making, installing, and maintaining their components, wind inconstancy generally means that almost every watt installed needs a second watt of standby gas power, and the things pollute viewscapes while killing thousands of birds.
You can't use green data either: those same sixties greens who hated nuclear also wanted immediate government regulations to protect the world from global cooling - and they've flunked every independent review of their ability to produce honest numbers since.
But how can the obvious: reduced energy use equals reduced pollution, not be true?
The answer is that reduced use does equal reduced pollution if that reduction is permanent, the capacity isn't taken up by another customer, and the volume change doesn't trigger a change in efficiency in the generation and delivery systems.
In reality these conditions are unlikely to ever be met - so the intuitive association between your reduced demand and lower overall pollution is correspondingly unlikely to be realized too.
Worse, the accumulated effect of thirty years of combined green and NIMBY politics means that your decision to use less power contributes to the continuation of an inefficient system - and that if enough people increased power demand to trigger system wide infrastructure renewals, that new energy would be so much cleaner that net pollution would decrease despite the increased output.
We know, broad brush, how the economic system reacts to changes in energy demand. In Adam Smith's universe a population decision to reduce energy use forces the industry to react to its own fixed costs by lowering prices - and that causes consumption to increase and therefore prompts renewed investment in infrastructure efficiency.
I don't know of any free markets in energy, but the same effect drives regulated markets except that the regulatory constraints on system change prevent continuous price and supply adaptation - meaning that these stresses build up until they trigger traumatic change.
For an analogy: think of planetary plates colliding along price/supply fault lines with regulators preventing continuous slippage through micro-seismic events until stresses build up enough to force a cataclysmic breakthrough.
So how do you reduce the impact of a future earthquake? by triggering it before pressures build to catastrophic levels - meaning, on the other side of the analogy, that widespread demand for more power now should reduce the economic dislocation to be created when the inevitable supply panic eventually sweeps away today's regulatory dam.
There's a traditional wisdom version of this: give a man a fish and you teach him to ask for more fish, but teach him to fish and you create a contributing member of society - or, in this case: helping a failing energy delivery system continue by reducing demand to meet its limits helps in the short term, but raises the barriers to be overcome before positive change can happen and thus makes the long term problem, and its effects, worse.
You get the same kind of effect when you intervene in civil wars to feed the starved and disposed - because a population decision to devote all available resources to killing each other means that new resources brought into the environment extend the killing and thus create, on net, more suffering for everybody.
And that brings us to the bottom line: nuclear power is orders of magnitude cleaner and safer than petrochemical generation - meaning that the sooner more of it comes on line, the less the power generation industry's long term impact on the environment will be, and therefore that plugging in an extra rack of Xeons may actually be better for the environment than almost anything else you could do.