I am also interested in this as it pertains to my fields of study.
I do know that CAS had an early love for things from the Near East- as evinced by his love for the Arabian Nights and work such as Beckford's Vathek and Rudyard Kipling's tales. Mention of this is listed here in Principal Facts of Biography by Donald Sydney-Fryer:
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www.eldritchdark.com]
Also, the poem to Omar Khayyam is indicative of this love. However, I do not know to what extent he had a knowledge of Sufism in particular. I assume he probably came in contact with it early on, but this is where my knowledge is limited to.
Anyone with more info, please let us know as I am very interested as well