I don't see why it wouldn't but I also wouldn't buy the factory brake controller; I'd buy a Tekonsha P3 or the ReDarc. The first is an industry leader and the second is an excellent system that can be all but hidden.
I like the plug and play ease of the Curt but decided against it for 2 reasons.I've been using the CURT Bluetooth controller and couldn't be happier. No wiring required and it can be used on more than one vehicle in the gargae.