That doesn’t sound quite right, if I may say so. What causes wind is a high barometric pressure in one area and a low pressure in another and the air rushes from the high toward the low. As it rushes through a wind farm it may be deflected momentarily by a windmill blade or a “stalk of asparagus”, but once it has passed the impediment the barometric pressures are the same as ever and it rushes on again, just as before.
You can think of a simplified model of it in this way [which is actually a valid physical metaphor]: When water falls over Niagara falls, it reaches the basin with an enormous kinetic energy. That energy has to be dissipated, and it is, through frictional forces, which not only heat the water but also erode the basin at the foot of the waterfall.
[This pressure, which arises from a gradient in gravitational potential energy, is no different from the gradient that arises between two areas of different barometric pressure.]
If you put a hydroelectric dam, or just a water-paddle in the falls, the water will arrive with considerably less energy when it reaches the bottom. But note: we haven't changed the gradient. The is still just as much of a potential energy difference at the top and bottom of the falls as there was before. This means there is going to be less water thrown up into the atmosphere as water vapor, and less erosion at the base of the falls because of the energy we've extracted to do work.
Same thing happens with turbulent fluid flow impeded by turbines when gases are involved. The pressure differential cannot be alleviated as quickly if we put a turbine in the way and take work from it; it will take longer to equilibrate, and there will be reduced wind velocity downstream. As a result, you may very well see weather changes downwind. Probably not... because we trap a very small fraction of the atmosphere's energy in a wind turbine, even an array, but there are still observable effects.