As you mentioned, the Chemical Marriage is an allegory. C.R. is not a man, but Man.
I wouldn't say they have had zero influence on society. Ben Franklin was suppose to be associated. I've heard rumors of Abraham Lincoln's involvement. In modern times, David Bowie was associated with the Ordo Templi Orientis, the cult that Crowley founded. Led Zeppelin's lead guitarist Jimmy Page was very into this stuff, and their music has had a profound effect. Others could be named.
AMORC is probably the best known, but they are pretty watered down. Their curriculum is very stretched out, and rather elementary compared with some more advanced groups. Spencer Lewis was associated with, I think, the Alpha et Omega, which was an early American Golden Dawn group that imploded from internal strife, and splintered into several groups, AMORC being one of them.
The thing to keep in mind is that all of these groups are lower level steps to much more hidden and secretive groups that only approach potential initiates after they have proven themselves amenable to the system in several levels of preparatory groups. Members are completely unaware (usually) of this, and most will never find out.
Freemasonry is an early example of these preparatory and filtering groups, though most, if not all of its current membership are unaware of this function.