It could be difficult. If the screen is glass, it would be impossible without serious damage to the puncher.
With LCD, it is possible to punch through it, but I really doubt it could be done easily. There are a lot metal parts which practically cover the entire inside (for grounding, anti-static and heat). I know the backside of an LCD is mostly aluminum, at least inside it is. The screen is also backed with aluminum.
Plasma screens have a thin glass layer. LCD screen are mostly clear plexiglass. CRT is glass.
Also, there is great risk for electric shock, as most monitors continue to hold a charge, even if unplugged for days. A CRT monitor could kill a person because the tube is vacuum sealed and WILL explode.