Theme Tweaker inserts text css blocks in the pages that your server dishes out. e.g.
<!-- Theme Tweaker (start) -->
<style type="text/css">
body {background-color:#E8E1C4;color:#1D1B29;}
...
</style>
<!-- Theme Tweaker (end) -->
It does not overwrite your style.css, which indeed it cannot, unless you have your file protection bits as 777.
Theme Tweaker only reads your main style.css file pointed to by:
$stylefile = get_theme_root() . '/' . $mThemeName . '/style.css' ;
It doesn't try to follow the @Import directives, so it may not work well for WP-MU.
I don't have WP-MU and haven't done any test on it. The only feedback I got from one user is that it did not work for him for a particular theme, although he says it worked for other themes.