This happens all the time, and is the reason for the rush of wind as the rain falls, and cools off the hot summer afternoon. In a thunderstorm which is tilted at the top away from the bottom, the updraft will go up at an angle, and the downdraft will come back down in a different location, making a nice little machine which wants to stay alive. The rotating updraft in a potentially tornadic thunderstorm can strengthen until the rotation reaches down to the ground. Most of the time it's a little tip of the rotation that hits the surface. Sometimes, however, the rotation is very large when it hits the ground, as happened the other day.
Many thunderstorms rotate.
Few produce tornadoes, which is where the rotation reaches the ground. A rotating storm usually produces large hail and very strong winds because the updraft reaches very high levels before coming back down. I have exhausted about all the knowledge I have about this subject. I am sure I will think of tidbits of information later, but this is the gist of the process. Probably way more than you wanted to know, and my teenagers complain to me about the same thing.