If you talk to any of the pre-eminent translators and practitioners of authentic Buddhist lineages, from any Asian-derived tradition, who were raised in Western Cultures, I am sure you will find very few who support your notion that Golden Dawn, or any other "mystic" or "occult" society, had any real influence in bringing the Dharma to the West.....and I'd bet that most of those people would also claim no influence from those societies, personally, as well. Maybe you'd find one, I dunno....I doubt it.
The spread of Dharma in Western Cultures occurred due to the existence of teachers (mostly Asian) who took the time and effort to teach interested Western students. Also, because said teachers took the time to educate themselves about our own cultural predispositions and worldviews. And because there were, and are, Western Students who had diligence and enthusiasm. It did not occur because some Westerners incorporated notions they thought were "Buddhism" into their own creative fantasies. My personal feeling, and this may be incorrect, is that it has only been in the last few decades that authentic transmission has occurred, in no small part due to the gradual "loosening" of the grip of Christianity and monotheistic faiths in Western Cultures. Certainly there are other factors--we live in a more multicultural world than ever before....
The Buddha turned the Wheel of Dharma three times, at least according to my (Tibetan) Tradition. Other Buddhist traditions may assert different turnings--I'm not that familiar with what the Thais, Sri Lankans, Vietnamese, Japanese, Laotian, Burmese Buddhists say about this..... But no Buddhist tradition asserts that any other religion or religious movement was part of any "turning" of the Dharma Wheel. HHDL, Kyabje Kalu Rinpoche, and many other masters have stressed respect for other traditions, and have pointed out the positive and beneficial factors and positions of other traditions. But every teacher I've met and studied with has not equated other religions with Buddhism.
According to a Khenpo I have studied with, there are two ways of "teaching the Dharma"--from a very public position, to "outsiders," wherein the commonalities between traditions are stressed, and the basic human values of compassion, love, nonviolence, morality, are stressed...and the "insider" position, which takes these values into account, but which stresses the differences, the "special teachings" or distinctive features of a tradition, those teachings and positions which differentiate that tradition from other traditions. But even from those who teach Buddhism according to the first position, and HHDL would be the primary example of this in the World at this time, there is always a clear differentiation, and clear statement regarding the necessity of maintaining one's tradition, and not mixing or confusing things.
As I said before, things may be similar, but not the same. It's important to understand both of these factors--the similarities, and the differences. But as an "insider" (the Tibetan term "Nangpa," literally translated, and multivalent but meaning "Insider" as well as "Buddhist") it is the differences that define us.