Considering that thunderstrikes makes sound, which is a form of movement in the air, it will generate some form of wind as well (following my logic). But can thunderstrikes cause/generate wind? And more importantly: Will the wind be noticeable?
Sound is indeed the movement of air particles - but on a small scale and more like a vibration. So the particles more or less stay at the same position but wiggle a bit back and forth around that position. You could say thats a "tiny wind" blowing back and forth with a high frequency, but thats not what we usually call wind.
What we usually call wind is a directed movement. This does not mean that all particles at every time have to move in the same direction, but on average they do.
Since a thunderstrike also causes heat and hot air is lighter than cold air, a thunderstrike also causes the heated air in its path to rise and other air around it to flow inwards. I don't know about the scale of this flow, but given the short duration of a thunderstrike and the surrounding thunderstorm i would say the amount of "wind" generated is negligible.