Yes they do :-)
I knew that when somebody left-clicks a PDF link (so it opens in their browser), it logs on WordPress.com stats. But I wasn’t sure about those times when people right-click and download the PDF to their computer.
So I ran a little experiment earlier and yes indeedy — PDF downloads DO also log on your stats. This is good news because it gives you an accurate picture of how many views your PDF documents are getting, regardless of whether your visitor views them in the browser or on their computer.
All the best,