I think that while LMP (UID) resembles Constantina and while there is a photo of her.With the ID of Beth Doe as Evelyn Colon, and the fact that Evelyn's isotope analysis was super inaccurate (saying she was probably a European immigrant when she was from New Jersey), I think it would do us well to step away from the definitive theory of this Doe being Greek.
The possibility that she is from the US and possibly local, is more plausible.