Short answer: no.
Other ideas:
Use CSS preprocessor
.leftmenu {
@include 'style.css';
}
This uses the nesting capability of CSS preprocessors to pre-qualify all the rules in style.css. Replace the @include with your favorite preprocessor's directive for bringing in another CSS file.
Rewrite CSS manually
You can "namespace" the rules in style.css by changing all the selectors to be preceded by a qualifyng .leftmenu.
Rewrite CSS automatically
You could write JS code to rewrite the stylesheet selectors at run-time to prefix the selectors with the class name, which his essentially what this plug-in does: https://github.com/thingsinjars/jQuery-Scoped-CSS-plugin. Or you could do this rewriting on the server, whatever language it's written in.
Use IFRAME as sandbox
If the content of the thing you want to apply the styles to can be placed in an iframe, you could add the style.css frame to the HTML loaded in the iframe.
That's about it.
