Since you haven't had any responses yet, I'll offer my opinion. I don't think the dealer would be too happy installing an OEM unit that you didn't buy from them because it puts them in a compromising position if anything goes wrong.
The scenario: they install a factory radio, but they have no idea where this factory radio came from nor whether or not it actually works--but they install it anyway. After it's installed it doesn't work. Or maybe it stops working after a short time. Who's liable? It's a factory unit but is it from an authorized source? Is it covered under warranty? Will the customer try to claim this under a GM warranty? Now to stretch things a bit more: Let's say there's a short in the radio unit itself that causes a fire. Who's to blame now? The GM techs who installed a part with unknown quality? Lawsuit, anyone?
Obviously, that's the extreme but that's what I would be thinking about if I were an installer who cared about getting the job done right. If the unit you get is brand-new and factory sealed, then there's less likelihood of objections. But if it's used, things aren't so clear. Besides, dealerships are not in the installation business. Because they are not just any old independent business, they have to be more careful about procedures and policy. It might be better (cheaper) just to get an aftermarket shop to install the radio for you.
All that being said, it won't hurt to simply ask your dealer how they feel about it
.
