Yes, but that is unnecessarily restrictive and assumes people will be using the privilege system in a specific way -- that is, nobody can post to it except admins.
Our privilege system has it's quirks, but it is highly customisable, and we wouldn't be able to know if we should show the button or not given no information.
For example let's say I want to have a category that only allows posting if you're a member of group A (and not registered users). If we set this "group X" to registered users, then the button won't show... but you DO want the button to show, just in case once you log in, you are in group A.
Hope that makes sense.