No. I don’t know of any browser (or other user agent) that associates any special behaviours with link query strings. The query string is for the server receiving the HTTP request to deal with.

As you say in your question, the target attribute is the method for controlling (or at least suggesting) what window the link should open in.

This is a trick,

function openInNewTab(url) {
  window.open(url, '_blank').focus();
}

// Or just
window.open(url, '_blank').focus();

In most cases, this should happen directly in the onclick handler for the link to prevent pop-up blockers, and the default "new window" behavior. You could do it this way, or by adding an event listener to your DOM object.

<div onclick="openInNewTab('www.test.com');">Something To Click On</div>

Reference: Open a URL in a new tab using JavaScript

If I get you, you want your link to open the page in another tab.

You may use the target attribute of the link like this :

<a href="somepage.html" target=newtab>text</a>

If you want something you can type in the URL field of the browser, that is a bookmarklet, you may use this :

javascript: window.open('http://www.dystroy.org');

In most browsers, ctrl-click a link do the same thing.

EDIT :

If what you can modify is only the href attribute of the link, you can make this href be like this :

 <a href="javascript:window.open('http://www.dystroy.org');" target=_blank>text</a>

If you can target your menu tag with jquery using its ID you can put something like this in an JS file that you'll add in your theme via your_theme.info

Drupal.behaviors.externalMenu = function(context, settings) {
    $('#menu_id').attr('target', '_blank');
};

Or you can use the Menu attributes module.