Yes I have seen images of the 2006 with the paddles but not for the Z06 as was mentioned.

The auto trannies on C6 use a new TCM controller for the C6's PCM no longer manages the trannie as it did for the C5s so you could not use the C5 PCM to control a C6 auto trannie

You'd have to swap to C6 PCM, TCM, and wiring harness since the C6 PCM now handles the TAC ( drive by wire) where on the C5 the TAC has its own controller.

Problem is there is no complete tuning product out yet to tune the PCM and TCM so I would not do such a swap until there is.