Can turbulence get blown into the path of an aircraft by wind?
Most certainly wake turbulence can be blown by the wind.
Simply put, we are trained to avoid flying into wake turbulence. Because it is nearly never visible, avoidance is either by time or position. We wait [minutes] for it to dissipate, or we carefully, and with good consideration, fly a path where it should not be. Certainly if I'm behind an airplane on departure or approach, I'll be hugging the upwind side of that plane/s path, knowing that the wake turbulence will be blown downwind - so far so good doing that. Once I flew out of position in a Cessna, formation with two other Cessnas. I was amazed at how forceful the wake of a same size airplane was! It was not good, and pretty well stood me on my wingtip. Happily, I had enough separation already that it did not create a collision risk.
But, when the airplane creating the turbulence is fast passing you, you have much less opportunity to maneuver to avoid his turbulence. If you were maneuvering a powerboat to pass another, you'd consider the effect of your wake on that boat, this is not much different.