I doubt George Washington was a memeber of the Enclave lol.
Still you are right the Enclave have a pseudo USA government going on. Still if you just look at it in terms of presidents that are members of the Enclave, there are only two known presidents and ones not even
Three if you include the pre-war president that took of to the rig before the Great War but we don't know his man.
Actually what I mean is that Richardson is President of
America, never once does he identify himself as President of the Enclave, in-fact he never even says the word (because it was primarily the name of the [censored] Oil Rig itself, ie, Control Station ENCLAVE, ENCLAVE Vault Control, "ENCLAVE here, why isn't you video feed working?" :swear:). The Enclave was the
shadow government, it had nothing to do with the official government at all; more than likely it's members were led by perhaps a council of the most powerful and connected members.
As far as I am concerned there is nothing pseudo about the Enclave, in-fact I would argue that, aside from the old name, the Enclave became obselete when the bombs fell and it's members actually
became the legitimate government, assuming of course, that all legitimate leaders not aboard the ENCLAVE were killed, Raven Rock was never used afterall; its function as a backdoor, secret puppet master ended and it simply was all that was left. We don't even know if the pre-war President was a member of the Enclave, Presidents come and go afterall.
EDIT: http://en.wikipedia.org/wiki/United_States_presidential_line_of_succession