Does the geometry of a lever alter the behavior of rotation

Here is a simplified example

If we consider that both A and B are the same body which is only free to rotate, F is the force acting at the exact same distance from that body in both cases, with the same magnitude and over the same period of time, will the body end up in the same ending position in both cases?

In other words does the geometry of the lever play any role?

Edit:
I forgot to mention, that we should also consider the lever to be weightless, as if it is not it will move the center of mass and the question is not regarding that, but purely dynamics of rotation.