Well that's an interesting problem.
This is quite simple in KDE, you just set up a special window assignment (right click the title bar) to make the terminal fullscreen, below all other windows, drawn without window decorations and to skip the taskbar. It works beautifully.
Under Compiz you can achieve a similar effect with CCSM with its Window Rules plugin. The problem you have is differentiating between a terminal you might load up subsequently and the one you load on boot. It might make sense to install another terminal application (Terminator is a fine choice) and just use that for your desktop. Then you can tell CCSM to change the window settings on all Terminator instances.
In both cases you can leave the desktop as it is. It'll be there, but it'll be obscured by the terminal.
Another way you could do this (using the same ideas as above but cross-platform) is to use
wmctrl to set the hints rather than leaving it up to the Window Manager.
The following three commands will set the current window to cover the desktop.
wmctrl -r :ACTIVE: -b add,fullscreen
wmctrl -r :ACTIVE: -b add,below
wmctrl -r :ACTIVE: -b add,skip_taskbar
You can either save that in a script or you can munge it all together in a lovely messy one-liner. Annoyingly, wmctrl can only do two hint changes at a time so it's a little more bloated than one might like.
gnome-terminal -x sh -c "wmctrl -r :ACTIVE: -b add,fullscreen,below;wmctrl -r :ACTIVE: -b add,skip_taskbar;bash"
Other terminal emulators will work like this but they might have a different argument for running something (vs the
-e, for example.