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These are the button actions available within InDesign (the middle group is SWF-only so they don't apply). So no, you can't set up an exit full screen or close document or quit.
However, Adobe Acrobat Pro has more options. You could set up the button's look in InDesign and then finish up in Acrobat. The available actions are shown in the list below, but pay special attention to the first one. Execute a Menu Item allows you to add any menu item to the button. (File > Close, File > Exit and View > Full Screen Mode)
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As Steve says, you'd have to do this in Acrobat but please keep in mind that there is no assurance that such actions will work in a browser, any non-Adobe reader, or on mobile devices.