Sag shouldn't be a significant issue with the shelf in question. It's going to be supported presumably at each stud, so the span is at worst 24".
Are you saying that a 1.5" thick torsion box would have 2/3 less deflection than a similar length and THICKNESS oak board? (If so, why is this true? I would expect it to be somewhat weaker than a solid piece of the same dimensions.) An inch and a half is too thick for this shelf. It would look ungainly. As I recall, deflection is inversely proportional to the cube of the thickness of the beam, so thickness is an important variable. A 1.5 inch thick oak board would have 1/8 the deflection (7/8 less) than a 3/4 inch thick board.
But to make the design the right size (about 3/4 inch thick) I'd presumably have to use 1/8" skins and the back piece would be 1/2 inch thick. How is this functionally any different than routing a 1/2 inch groove in the back of a solid piece of wood and using a cleat on the wall? How is the torsion box aspect of the shelf actually related to the hanging of it? It would seem to me that you can use this hanging scheme with or without a torsion box.