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.
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. 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.
A quick romp through the literature
Smith, Barthelmie & Prior used In situ observations of the influence of a large onshore wind farm on near-surface temperature, turbulence intensity and wind speed profiles. They found that in the daytime, there was no observable change in temperatures once they were more than 2km downwind from turbines. However, there was an increase in night-time temperatures at 2.5m above ground (hence the use by farmers of wind turbines for frost prevention)
On top of what I've written above, we've also got a bunch of modelling in the literature. Now, this is largely a bunfight between different assumptions: pick the answer you want, and tune your assumptions accordingly. However, these papers are written by people with different axes to grind, so you'll find a range of possible outcomes, and you can decide for yourself which assumptions are more or less likely.
Mark Z Jacobson wrote the book on the Fundamentals of Atmospheric Modelling, and tends to build up from the micro level. A recent paper of his shows potential benefits of reducing the energy in hurricanes that reach the shore, and we know that the first-order impacts of that would be positive.
Roy & Traiteur looked at Impacts of wind farms on surface air temperatures and found significant very local effects, and options for mitigation.
Wang & Prinn looked at potential long-term global impacts of multi-terawatt-scale installations and found that massive onshore wind turbines might cause some warming over land (though less than the coal & gas plants they would replace), and massive onshore wind turbines might cause some global cooling. The modelling was done by assuming the turbine interactions would behave like a generic increase in surface roughness; the other key assumption is that the loss of detail from meso-scale modelling did not significantly impact the results.
Kirk-Davidoff and Keith, like Wang and Prinn, used coarse meso-scale modelling by adding anomalies to surface roughness coefficients. With continental-scale windfarms, they found very little change in global temperatures, but local changes could be up to 2 Kelvin.
Rooijmans' Masters' thesis (Universiteit Utrecht, 2004) looked at the impact of a huge (9 000 km2) offshore wind farm on patterns of rainfall, using a mesoscale circulation model, and found that the distribution of precipitation could change, with more rain at sea, and less onshore. That modelled windfarm would be about four times the size of the largest envisaged offshore wind farm.
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: you can even (HT scruss) buy wind machines dedicated to producing that turbulence in no-wind conditions (these wind machines, ironically, are typically powered by fossil fuels).
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.