Yes, you can do this with Fusion 360 Simulation. Use the "Angular Global Load" and apply the rotation velocity and acceleration, if applicable, to the circular frame. Use the "Axis" Direction Type and select the outer or inner circular face of the frame. It would be best to exclude all other components from the simulation to simplify it.
It's also important to properly constrain the rotating component using a Pin constraint. You likely want to constraint it axially and tangentially, but not radially.
You mentioned that the circular frame is a good candidate for thin shell elements, but Fusion Simulation doesn't have that capability yet. It should still solve fine with Tet elements, just make sure the mesh is fine enough so that you have a minimum of 3 elements through the thickness of the geometry.
Tyler Henderson
Principal User Experience Designer