Think of the tube of a monitor/tv as a capacitor. To discharge the capacitor, you don't need a path to earth ground, you need a path to the OTHER LEG of the capacitor. Now in the case of a monitor, the 'other leg' is usually tied to earth ground (and generally the metal framing of the monitor).
Now, as to leaving it plugged in: If you are sure that both hot & neutral are cut off by your switch, then leaving the earth ground connected between the monitor and the real world certainly won't hurt anything, but it's not required to safely discharge the monitor.
Neutral is not switched in domestic outlets, and nor does it need to be. The voltage potential between neutral and earth is ZERO VOLTS. They are connected together in the switch board on any MEN system.
As for the capacitor theory, all well and good, but the other leg of the capacitor in this case is NOT the metal chassis, it is the cathode in the neck of the tube. Remember you dont need to touch both legs on a cap to get a boot from it, and in the case of a CRT, it is charged through the HV transformer, which is an isolation transformer, and hence, has no reference to earth. So touching either the anode OR the cathode may indeed cause a substantial electric shock as both will be at a different potential to earth. Discharging the anode will in this case be sufficient. This is not like a capacitor that has one leg connected to neutral.
Cheers mate, that's kinda what I figured. Was just a bit puzzled by various videos like this one
http://www.youtube.com/watch?v=mV9Td8vAb0Y which say to unplug the monitor. Is that cause they don't have switches on plugs in the states or something? Just doesn't make sense to me as I know a little about electrical theory etc (i'm a domestic electrician by trade) an I couldn't figure out how it could work without the neutral/earth plugged in.
No problem, i figured you mustve had some electrical knowledge behind you. I would say that it may have something to do with the lack of an isolating switch on US socket outlets yes, and im not exactly sure how their protective earth system works over there either, largely cause i have no interest in it.
I am pretty sure the system you have over there is very much the same as the system we have here in Australia, being the MEN system, or multiple earth/neutral. Every installation has an earth stake driven into the ground connected to the main earth bar in the main switch board, the main neutral bar is also connected to the main earth bar via the MEN link, and serves to keep the neutral line at the same voltage potential as earth. The protective earth is there to carry current ONLY in a fault situation, and to provide effective operation of the circuit protective device ( be it a fuse, RCD, ELCB, RCBO, or MCB ).
In the case you want the protective earth system to bring the anode of the CRT down to earth potential, which will then make it safe to work on.