Don't misrepresent where you went to school.

[alexf.1990]

Are HES allowed to join the Harvard Alumni Association upon the conferral of their degree?

They are. They're also allowed to join the Harvard Club. From what I understand, the HAA isn't as valuable for networking as the alumni associations of the individual schools. The Harvard Club appears to be just a social club for people who graduated from Harvard College to talk about the good old days, so membership isn't worth much for someone who can't bond over experiences on Harvard's campus.