After the transfer has been approved, the C&R FFL holder can travel to the seller's state and pick up the gun and take it back home. That is true whether the seller is a dealer or an individual. It is also true, from a federal standpoint, for other guns. A Federal licensee can buy guns (within the limits of his license) anywhere in the U.S. unless there is some state restriction, and take them anywhere in the U.S.
I sold a C&R NFA firearm to a C&R holder who is a resident of a nearby state and wanted to deliver it. I called BATFE to see if I needed approval to transport the gun but the agent gave me his name and said an verbal OK was good enough. In one case, the C&R holder came to my house and picked up the gun and took it with him. He didn't need approval to transport the gun because he was an FFL (C&R license) holder.