Analysis of information sources in references of the Wikipedia article "Cry of the Banshee" in English language version.
Apart from some a spurious salute to the author's poem, The Bells, in Cry of the Banshee's pre-credit sequence, there's no reference to Poe.
It is still possible to write Poe's name into a movie title like a possessory credit, even in the case of films he had nothing to do with (such as Edgar Allan Poe's Cry of the Banshee)