@Craig: I would say it doesn't affect responsive design at all. It just reloads the markup – all the css, including media queries, will work as normal. Accessibility should really not be affected either. Screen readers usually have the ability to detect content that is added dynamically, and pjax falls back to standard page loads if the client doesn't support it for some reason.
@Vikky: Hm. You're right. Occationally it seems to do full page loads, seemingly at random. Maybe it happens if you click a link before the page load is completely done?