Leave it in the case.
You probably won't save that much space.
However, I looked at doing this with an old Pentium M laptop & determined without a docking station I still needed to open the lid, turn on the PC, & manually hit the key combo to turn on external monitor.
Don't know if this the same with yours.
Also, irotate is a good tool for laptops with older ibm graphics that don't give you the option to rotate the display.