I hear you and understand it is a separate Order but it's safe to say anything Crowley had his hands in was HEAVILY influenced by the HOGD. Qabbalistic TOL and ceremonial "magic(k)", not to mention the HOGD is often considered AA's predecessor. If there is no HOGD then it's safe to say there is no AA.
True. AA was established in a way that to avoid the infighting of HOGD. However things like crossing the abyss and certain other things within the system is original.
While HOGD was a big influence, the system is highly modified in a way that makes it stand on its own.
I wanted to mention the theosophy definition, but just to put into context what it is like researching these things, this subject is about as historically accurate as the movie 300. People will stake claim to things or say things to fit their narrative and agenda. The "Cipher Manuscript" alone...come on, they themselves were a little fishy to say the least yet GD members rarely question their origins or authenticity.
Im not saying that GD is the whole rosocrucian body.
"the Rosicrucians were Theosophists, religious men whose doctrines were of spirits, of the elements, of numbers and heavenly bodies and their influence on men" is what Im talking about. The teosopy that influenced the rosocrucians was Böhmes, wich is more complex and more focused on the internal.