Drone gyroscope placement
In an ideal world, there's no difference between placing a gyro at the center of mass or at the very end of an arm. In practice the frame might flex under flight loads, causing a different angular rate at different sensor positions. The gyros are also not perfect, and the linear acceleration experienced by the chip will couple to the gyro outputs, but this effect should be neglible in practice.  

The real issue is that if the IMU chip isn't located at the center of mass, any change in attitude will register as an acceleration. For example, pitching up might register as a downwards acceleration. Thus while the three axis of angular velocity might not care about sensor location, the three axis of acceleration will.
If the distance of the IMU from the center of mass is known, you can cancel out the angular acceleration - linear acceleration coupling with some trigonometry.