Brian,

We are towing a '06 Hummer H3 and I think it is built on the same body as your truck. Once we switch the transfer case to neutral, we remove the key and lock the doors. The steering column does not lock and the tires move as they are supposed to. It would be easy for you to confirm this empirically with a lift or jack.

As a matter of fact, I made the Hummer dealer shift the thing into neutral and push it around the parking lot before I bought it.