Yes and no. All the common web browsers has a security measure to prevent that. The goal is to prevent people from creating replicas of websites, change the URL to make it look correct, and then be able to trick people and get their info.
However, some HTML5 compatible web browsers has implemented an History API that can be used for something similar to what you want:
if (history.pushState) {
var newurl = window.location.protocol + "//" + window.location.host + window.location.pathname + '?myNewUrlQuery=1';
window.history.pushState({path:newurl},'',newurl);
}
I tested, and it worked fine. It does not reload the page, but it only allows you to change the URL query. You would not be able to change the protocol or the host values.
For more information:
http://diveintohtml5.info/history.html
https://developer.mozilla.org/en-US/docs/Web/Guide/API/DOM/Manipulating_the_browser_history