Clearing a System.String in C#

Will this overwrite the contents of my string:

unsafe
{
    fixed (char* chars = str)
    {
        for (int i = 0; i < str.Length; i++)
            chars[i] = '1';
    }
}

The background is I'm using NetworkCredientials, in which you set the password using a plain old System.String. I'd like to "clear it" afterwards, if that's possible. Any suggestions on how to do this are welcome, but the main question is to understand if fixed will really give me access to the underlying char array. Thanks!

Edit

I would like to understand what is going on here - if a string object is immutable, and fixed doesn't let the object move then what's happening in the code posted? Where are those characters being written to?