You're not too familar with the inner workings off an open differential are ya?
Yes, the inner shaft would spin the correct direction, but neither wheel would actually receive power if it were to need it. If you removed your rear driveshaft, left the CAD unlocked, put it in 4wd, and tried to drive away, you wouldn't go anywhere.
The spider gears would just cause the inner shaft to spin. The R&P would be spinning, 3 of the 4 spiders, and the inner shaft. That's it.