Yes, but StaticMeshes have materials on them too. In my case I have a StaticMesh which contains glass, but the glass casts shadows as if it was solid.
Now, I could split my StaticMesh in two seperate models, one for the glass and without the glass, but if there was a possibility of making a material not cast a shadow (like a texture with a completely transparent alpha channel or the black parts of a masked texture) I could just apply that to my glass.
It's possible to turn off the collision per material, so I figured it might be possible to turn off that it can cast shadows.