If you load http://example.com and the HTML there includes an image tag that says '<img src="http://othersite.com/image.jpg">' it means your browser will connect to othersite.com and ask that site for the image. It will not ask example.com.
You can't use <object>, <iframe> etc tags to embed pictures in your Github README, so you don't get automatic updates there no matter what (i.e. images would only refresh on page load). I don't know if Github proxies and caches <img> contents, or how long they cache it for but I haven't personally seen any delays when I've updated images used in READMEs.
But to repeat: auto-updating will not work for Github-hosted content AFAIK.
