Yes but not for the same reasons.
Ever hear of the "Hall Effect Sensor"?
If not, then this page will get you started:
http://en.wikipedia.org/wiki/Hall_effect_sensor
Hall effect devices are basicly transistors with a magneticly sensitive base lead while a normal transitor will have a wire connecting the base to the emmitter and collector junctions
However EVERY transistor and EVERY diode can be affected by magnetic fields, to some degree, this is why you take of your electronic watch when you get a CAT scan because the scanner has an enormous magnet in it
What happens is that in a hall effect device it is optimized to sense magnetic feild changes, and what happens is that when you bring the correct pole of a magnet into proximity of the hall effect device (transistor) it turns it on, when you turn the magnet around the other way, it will shut the hall effect transistor off again.
Now your LCD screen although the screen has mainly Liquid crystal semi conductors in it tends to respond to some degree in the same way mainly for 2 reasons.
Liquid crystals are EXTREMLEY sensitive to electric field changes, so you don't even need a magnet to see how sensitive they are. Try this; put a piece of "scotch magic brand" (tm 3M) tape (the kind you can write on) and stick it LIGHTLY onto the face of your LCD screen, leaving one end NOT stuck down so that you can pull it back off.
Whith the monitor UNPLUGGED and the VGA connector OFF rapidly pull the tape off at about a 45 degree angle away from the LCD screen.
You will see many of your LCD "pixels come to life"
That is just from non-contact static electricity.
Now if you were to take say, the magnet out of the magnetron in a microwave oven and pass it over a running LCD monitor you may induce enough magnetic pressure to short out the transistors and diodes in the Liquid crystal display (that is the first method of magnetic interaction -- I said there were 2 remember?)
The second method that the magnet will cause problems is for the same reason that motors spin.
If you MOVE a magnetic field across a conductor like a wire or a circuit trace (and there are 10's of thousands of circuit traces embedded in the LCD screen) then you will magnetically induce an electric potential on those conductors and circuit traces -- you might short stuff out by turning something on when something next to it should be off
Bottom line?
Don't do it