You probably can't get the functionality you want without making some edits to Unity itself. (Requires programming knowledge)
There's no clear way to tell the difference between the two cases. Either Unity can bind to key press/release events on Super (which won't see other keys being pressed while it's held) or it can bind to key combinations, in which case it won't see Super except as a modifier on whatever key that was pressed in combination with it.
It should, theoretically, be possible to achieve the functionality you want by having Unity use XGrabKeyboard when you press Super and and XUngrabKeyboard when you release it, but it's not exactly common to go whole-hog on it.
What I usually see in things like IceWM and Windows is for there to be a global keybinding on the Super key and then local keybindings on the window that it calls up for things like Super+R (Windows Run... dialog) and so on.
My advice would be to rebind your launcher shortcut to something almost as easy to hit as a bare Super. (I use Super+Space for the copy of gmrun I use in Lubuntu which matches nicely with using Ctrl+Space and Alt+Space for other launchers like SiteLauncher in Firefox)
Best Answer
You can change that in Compiz.
Install
compizconfig-settings-manager
Hit Alt+F2, type
about:config
and hit Enter to open the Unity configuration.Or run
ccsm
on the command line.Change or disable the shortcut for Key to show the launcher as you like to free your Super key: