I agree with @justynjj. It's not well adapted to the desktop environment. Pull to refresh has been created because of the momentum scrolling (we could see past the top of the page after scrolling quickly so it was decided to use that space and natural movement to add a function).
The desktop equivalent, in my own opinion, is the "auto-load" at the end of a page. If your content scrolls in the other way (most recent on top like Twitter), you could just detect the scroll event while at the top of the page -which hook does, I believe- and load new content with Ajax. Refreshing the whole page isn't going to cut it in many cases I believe.