C# alone, the answer is no. The given code only start the Browser process, but not actually doing anything with the browser control.
You may use
HtmlPage.Window.Navigate(new Uri("http://stackoverflow.com/"), "_blank");
which will open on a new ab on IE.
you could try set your default browser to mozilla, but I am not sure if this will work.
reference:
http://stackoverflow.com/questions/16106503/htmlpage-window-navigate-opens-a-new-page-or-new-tab-on-every-click[
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