I have not been able to tell on cursory investigation whether Potocki was known to Burton. One point of convergence however is found in town of Saragossa itself. Burton was deeply interested in Abulafia of Saragossa. That Patocki chose to place his fictional manuscript there may also have meaning since his book deals with secret societies and the Kaballah. It is said that Patocki may have been a Free Mason. One might look therefore for secrets coded in The Manuscript Found in Saragossa.
Although I know nothing personally concerning the secrets of masonry, one does read tracts by those that have claimed to expose them on heretical grounds. At the time of the Templar debacle they were accused of anti-Christian, profane Muslim-related practices, and of holding the belief that Christ was a mortal being. One reading of Patocki would be that Alphonse is going through the typical masonry initiation, experiencing a simulated death on the gallows, and being reborn into a Templar/Muslim remnant society.
Alphonse, the naive young officer whose story the Saragossa Manuscript tells, is half Muslim, half Christian by birth. His chief concerns, when confronted with multiple requests for him to convert to the Muslim religion are that he maintain both his honor and his Christian heritage. He manages to embrace the idea of being married to two Muslim brides however without much trouble. His chief virtues in the eyes of his Muslim evaluators are his ability to keep secret information secret, and his courage. With secret societies I have always felt that it is not the actual content of secrets that is important, but rather the secrecy itself which lends a sphinx-like seal of potency to those that hold the secret knowledge.
Despite the fact that a main character is a Cabalist (ah spelling choices!), not much is revealed as to the nature of the computational studies he performs. There is a geometer however whose rambling mathematical musings may contain hidden meanings for those who know how to read them. I do not. The geometer's remarks are entertaining even on the surface level as a modern voice informed simultaneously by an engineering and a philosophical approach to life.
The secret gold mine of the Muslim underground society is said to have played itself out at the end of the novel. The mine's shafts are flooded with water to hide them from prying eyes. This is strangely reminiscent of the Oak Island site said to contain Templar gold. Is the Manuscript Found in Saragossa a treasure map? Is it a Templar Manifesto? Is it the product of a man whose musings on the history of relations between Muslims, Jews, and Christians turned him into a werewolf?
Ah, who am I to spoil your fun!