Probably yes. Have you seen screen cast o matic .com? They allow video recording without installing any plugin just visiting their website. So if that can be done then yes Screen sharing too.
Sorry I exactly dont know how do they do it. Please try out. They use some kind of Java plugin (not alone Java Script).
If you're using chrome, you can share your screen using WebRTC to other browsers that support it. Right now, that's just Firefox and Chrome.
Check out talky for an example. https://talky.io
Wouldn't it be a pretty bad security hole if your browser - the one program on your machine that the most people are trying to exploit - could access parts of your screen that are outside its own windows?