If the template is active, then it should be read, just like your main stylesheet.
Style will "cascade" to that stylesheet.
There is an entry in the wiki on how stylesheets cascade in zen, or maybe in the tutorials, I don't remember exactly.
Bear in mind that some settings in your main stylesheet will override the menu's stylesheet.
It's against the "cascading" logic, but ZC is not HTML but a PHP app.
Bottom line, if it reads your main CSS, and both are in same directory, it should read your menu stylesheet, otherwise your ZC is corrupt.
Make sure that the template where both are is active, you may have them together in an inactive template.
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