From my experience (with the illuminated front black bowtie) the dealer couldn't see anything, and the chat people said I had to contact them. When I told the chat people on Chevy's accessory website that I was getting the run around, they were finally able to look into it a little bit more, at least enough to tell me my order had not shipped yet.
They charged my card the day the order shipped to my dealer for install. So if you have been charged, it should be on the way!
You can get a full refund from the dealer (including installation), as long as there aren't special order parts.