It doesn't trump the ability to record stats. When it comes to business there are certain things you can't do without, for most sites (that are big enough to matter) stats are absolutely required, no improvement on usage would be worth losing stats for.
(Not talking about this project in specific as it seems stats can be made to work with it, just replying to the idea in your comment.)
Server-side, yes. Client-side (Google Analytics, etc.), it may need adaptation. See the section “Dealing with scripts” at the bottom of http://instantclick.io/start.html
I haven't read the source for the linked library yet, but could you just have javascript in your pages that hits a /gen204 page on your site when the DOM is ready ? Then the preloaded page will only hit the /gen204 if it's actually rendered. Then just count the 204s instead of 200s.
