The short answer is yes, it's possible. And it can also reduce harm.
###Summary of the changes
Here's a brief summary of the changes that happen when electricity is generated from a wind turbine, rather than from a fossil or nuclear plant:
- energy is taken out of the wind further upwind than it would otherwise be
- there is more turbulence just downwind from the wind turbine
- less low-grade heat is put into the environment around the fossil or nuclear plant that has been turned down, or off, because the electricity is supplied from wind now.
###Global impacts As far as we can tell it's unlikely that there would be global effects at any plausible levels of global deployment (let's say, up to terawatts of mean power, but below tens of terawatts). But a single row of turbines can be enough to cause very local effects, and those could be positive or negative.
There is an open discussion in the literature about what the impact of removing terawatts of wind power would be (references to follow - please ping me in the comments if I don't add these in in a day or so). But it's a theoretical discussion, and not really meaningful, because it would absolutely depend on where the power was extracted.
###What happens to the wind's energy?
Ultimately, pretty much all energy in the wind ends up as low-grade heat. And that's regardless of whether or not it gets there via a wind turbine or not. If not, it will eventually dissipate due to friction, where it becomes ambient low-grade heat. If it is, then it will get converted into electricity, then some energy service (e.g. lighting), and then ambient low-grade heat.
So deploying lots of wind turbines just moves where that energy gets taken out of the wind, but not how much.
An unshrouded turbine can extract at most 16/27ths (59.3%) of the wind's kinetic energy - that's the Betz limit. In practice, it's more like 20-50%. Here's the power curve for an E82-Enercon 3MW turbine, from the Enercon brochure:
The lighter curve, plotted against the vertical axis on the right, shows the proportion of the wind's kinetic energy that is converted to electricity. At around 9 m/s wind speeds, that proportion maxes out at about 50%. A further small (~2) percentage goes to internal conversion losses within the turbine.
###What are the energy changes, and where?
The full picture is more complicated. Whether switching from fossil/nuclear to wind would change patterns of energy service demand, and energy efficiency, is an open question, so there are plenty of ripple effects. But, putting those aside to simplify things, just switching from fossil/nuclear to wind wouldn't create new sinks for the low-grade heat: lighting would carry on getting used at the same time and place as it does at the moment. What would happen is that energy would be extracted from the wind in new places: at turbines, rather than further downwind where the energy would be dissipated by friction. The other thing that would change is that there would no longer be additional sources of low-grade heat at all those fossil and nuclear power stations. Now, they're pretty intense sources of heat: nuclear or coal plants typically push out 150% - 200% as much energy as local heat, as they do electricity. So that's a signicant input of heat into a local weather system, which would no longer be there when they're turned off because the electricity is being supplied from wind instead.
###Consequences and conclusions
Distributions of heat affect weather and climate. So, deploying lots of wind turbines can change local patterns of evaporation and rainfall. They can also change patterns of frost: the turbines increase the turbulence in the flow, close to the ground, reducing frosts: there are farms that deploy turbines in order to harness that frost-prevention.
So that's the ultimate change: energy would be extracted from the wind further upstream than it was previously; and there's less heat put into the system from the cooling systems at fossil and nuclear power stations. These are all local weather effects, and could be beneficial, harmful, or neutral.