You can't style by user at all, so no. There are some Theming add-ons that might be able to help you in some ways (I know Themebuilder can change things according to who the user is, and the others might be able to do something similar too)
This is a bit of an unusual request though (which is why you can't do it natively). Most users would expect to visit a website and have it look and feel the same whether they are logged in or not. By all means, change all the options and menus when they're logged in, but not the look and feel controlled by the css.
We had to do something similar so we just built a custom theme plugin that would display certain things depending on whether the person was logged in or not. Nic is right though that Theme Builder offers the same capability and is an easier solution than having to build a plugin.
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