I mean "Yharnamite" as in "person who has received blood treatment"; I primarily use Yharnamite as a descriptor for a particular state of existence rather than to refer to simply a person living in Yharnam (which is also why, in the OP, "Yharnamite" is listed under "race" separately from "human"). And yes, Gilbert was definitely a foreigner of some kind, I'd say. Whether he had an association with the Healing Church is a bit more open to interpretation, but yeah, Flamesprayer does suggest that he had been involved with them somehow. Maybe he was a low level cleric of some kind, since there were apparently a lot of things that the church never deigned to tell him? Or maybe Gilbert knew, but didn't want to betray the church by telling the player?

So much is open to interpretation in Bloodborne... it's great.