No, twisting a firm rod, regardless of its length, would not allow for the transmission of information faster than the speed of light. According to our current understanding of physics, information cannot be transmitted faster than the speed of light through direct physical interactions.
When you twist one end of the rod, the atoms or molecules at that end will interact with their neighboring atoms or molecules, causing a chain reaction that propagates along the rod. This propagation of the twisting motion is limited by the speed at which atoms or molecules can interact with each other. These interactions happen through electromagnetic forces, which propagate at the speed of light.
So, when you twist the rod, the information about the twist will indeed propagate along its length, but it will do so at a speed determined by the interactions between atoms or molecules, which is significantly slower than the speed of light. Therefore, the twisting of the rod cannot be used to transmit information faster than light to someone on the other end.