As the others have stated, by all means you can but i wouldn't rely on the monitor's speakers, as the sound plays with no bass. Resulting in only high frequencies. So unless you/anyone can bare/ put up with such frequencies, then the monitor's speakers will suit you...except for those moniter's that have a built-in TV tuner. The speakers for those models have roughly 5-8 watts of power.
If you go the monitor route, as the op stated, getting a pair of speakers (depending on your budget) will work, as long as you purchase a 'Y-cable' as well.
*Edit: Fixed error.
By the way, I'm trying to help anyone through passed experiences of my own and 'recycled knowledge' collected from others.
If you have any others concerns/questions, by all means you/anyone can ask in these Forums. As long as there is 'no existing thread' present.
You can also send anyone here a Personal Message (PM) in regards to your dilema. Take care & don't forget to always have fun!