Yes, absolutely. The theme of sanity vs. the loss of sanity would be a leading theme choice of mine. There is a lot of support from the actual text as well. The word "mad" or "madness" is used 7 times. The narrator of the story is constantly trying to convince the reader that he is not crazy at all. He constantly reinforces the idea that he is sane because of how carefully he planned and executed his murderous plot.
Ha! would a madman have been so wise as this,
Of course the first lines of the text tell me that the narrator is a complete nut.
I heard all things in the heaven and in the earth. I heard many things in hell.
The narrator claims that his illness/disease granted him the super power of super hearing. His hearing is now so powerful that he hears voices from heaven and hell. Yep, that sounds like crazy man talk no matter how many times he claims that he's perfectly sane.