the BW 1356 transfer case does not care what trans is bolted to it. both the E40D and C6 trans were bolted to the 1356 T-case, so you are good to go. the big difference is the E4OD is electronicaly shifted, and the C6 is mechanicaly shifted.
to make the C6 work properlt you will need a VRV, ans a downshift linkage.
other than that, it is not a big deal.