If the monitor has the correct connections it can. For example the Samsung T240HD has component in connectors as well as HDMI which most modern DVD players have. However if the monitor only has a VGA or DVI input things can be a bit tricky. You'll need to hunt around for a converter box mostly likely.
Do it, but I can't vouch for the quality. Usually you need a box to convert the signal in real time and those can be expensive $100+ easily.