Is it possible to get a browser window to update while it is in a Javascript loop?

You need to replace your synchronous request with an asynchronous request and use a callback. An oversimplified example would be:

obj = do_async_ajax_call(function (data, success)
{
    if (success) 
    {  
        // continue...  
    } 
}); 

function do_async_ajax_call(callback)
{
    var xhr = new XMLHttpRequest();
    xhr.open("GET", "http://mysite.com", true);
    xhr.onreadystatechange = function ()
    {
        if (xhr.readyState == 4 && xhr.status == 200)
            callback(xhr.responseXML, true);
        else if (xhr.readyState == 4)
            callback(null, false);
    }
    xhr.send();
}

This way you're passing an anonymous function as a parameter to the ajax requesting function. When the ajax is complete, the function that was passed is called with the responseXML passed to it. In the meantime, the browser has been free to do it's usual thing until the call completes. From here, the rest of your code continues.