What I've seen of the Classic Controller is pretty damn close to the SNES controller design. But I don't have one.
But yes, the VC does not remap the buttons, they correspond to the same buttons on the GC controller as they do on the SNES controller. But VC games that don't use the remote emphasize use of the Classic Controller (they will show "You will need the Classic Controller." with no mention of the GC controller).