Get current browser DOM with jsdom?

Is it possible to get the changed/live DOM of a website with jsdom?

For example:

Client

In my test.html file I have a button, which appends new <div class="p"> elements:

$('#button').click(function(){
 $('body').append('<div class="p">new</div>');
});

Then I have another button that calls a function on the server (with NowJS or Socket.IO).

Server

In my server.js file, now, I want to count all the appended div elements with the class="p":

everyone.now.countDiv = function() {
    var jquery = fs.readFileSync("./jquery16.js").toString();

    jsdom.env(
      {
        html: 'http://localhost:8080/test.html',
        src: [
          jquery
      ],
      done: function(errors, window) {
        var $ = window.$;
        var len = window.$('.p').length;
        console.log("Divs: ", len);
      }
    });
}

I know that I could count the elements on the client side and pass it to the server. But I am interested if jsdom can access the "new/current" DOM.

I assume jsdom reads the DOM of the text.html, but can't access the live DOM of a website!?