The Falcon is, certainly, recognizable as a Correlian freighter. Anyone who knows the ships of their galaxy will recognize the mechanisms littering the outside of the ship as components from that world. The shade of the metal composing the body, also recognizable, even if she couldn't place the exact model.

They don't make them like that anywhere else, but on his home world, and Han would be happy to jabber your ear off as to why the best ships come from there.

As it is, Han is close enough to the ship, still, to be by it ... if, let's say, someone was inclined to find the ship and it's captain.