Are the polygons that fall within the alpha range of the Cutout Standard Shader rendered?

For example, I take a cube, make one of its faces transparent, and assign the Cutout Standard Shader to it. Is that face still being rendered?

If so, how expensive is the performance compared to the cube’s all other faces?

Yes it is still rendered and has almost the same overhead. You might save a bit fillrate since the cutout shader won’t write to the frame buffer when a fragment is discarded. However every fragment(pixel) is still processed.