Yes, this is the famous author who created Sherlock Holmes and yes he wrote a book about fairies. As it says in the introduction in the link provided, Sir Arthur came to appreciate spiritualism and the occult and around this time the Cottingley hoax came into being. He obviously believed it, as the writing of the book would imply, but I think that things like this aren’t so much a show of gullibility as it is a display of one’s desire to believe. It might not be as exciting or ground-breaking as Sherlock Holmes was, but it is good for historical purposes and it also makes for some interesting cocktail party trivia.
Here’s a link to an online text of the book