No you can't. F11 simply removes the address bar at the top of the screen.
Wrong. F11 works for me exactly the way I suggested. I leave its Auto-hide feature unchecked. Press Alt-Space H while you are in Fullscreen mode if you would like to use it that way too.
Default is full screen with no way to minimize or move the open window.
In fact there is a new feature apparent in IE10, available via right-click of the window's thumbnail in the Taskbar. Then even though the window's Maximize option is greyed (indicating that the window is already in that mode or in Fullscreen mode) its Move
option is inexplicably active. When I use it when the window is actually in Fullscreen mode toggled out of its normal mode it is instantly toggled back into its normal mode--so the same effect as using F11 on that window without actually even having to have
that window in focus. YMMV.
As a test of a combination that I would never use myself I just put a window into maximized mode (e.g. via Alt-Space x) and then applied Fullscreen mode to it. In that case I can still use the new feature of using the otherwise inexplicable Move command
to get it out of Fullscreen mode without having the window in focus but of course then it only switches the window back to the maximized mode, e.g. its Restore option is still available and its Move option is then finally not available. YMMV.
In all cases that a window is visible Minimize is always available as an option. In fact, it is bolded indicating that it is the default option although that has a different meaning if there is more than one tab. E.g. with Taskbar preview in effect,
I then see that the current tab stops being selected even though the tab that was "minimized" is still showing. YMMV.
If you need help understanding your window states please describe them in terms of the state of its window menu options. Except for the Move command being available when the window is in Fullscreen mode they allow you to infer the actual window state,
in particular whether you are looking at a window in its maximized state versus a window which is in its normal state but maximally sized. The latter case is then seen to be just a less usable variation of its normal state. E.g. then all its options except
Restore are available because it is already in its normal state. In particular Size is available then so it can be resized to something that is more usable. So then if you really want to see it take up the whole screen you can do that by toggling it into
Fullscreen mode by pressing F11. ; )
FYI
Robert