No, in thinking that they matter so much that using an arcane typeface that no one has ever heard of will be a difference maker. But I somehow think you would wear that distinction as a badge of pride.
I’m not necessarily arguing that it will be an automatic difference maker. I am saying that good typography and page layout will affect the way people respond to a document, and good typography includes appropriate type selection. Also, the fact that none of the typefaces I mentioned are included for free with popular computer products does not mean that they are obscure. Minion, Bembo, Sabon, and the various flavors of Garamond are mainstays of book printing. Anyone who has read more than a handful of printed books in the last 20 years or so has almost certainly read something set using one of those typefaces. For example, every Harry Potter book sold in the United States was printed in Adobe’s version of Garamond.