I played on a 20" monitor with the same res. A large part of it depends on whether your monitor supports 1:1 pixel mapping or 16:9 resolutions. A PS3 displays at 16:9 so if your monitor doesn't support it the image will be stretched vertically by 1/9th.
With that said, my monitor didn't support either of those so the image was stretched and it still looked pretty damn good imo. Played Drakes Fortune, DMC4 and Super Stardust HD for a huge amount of hours before i eventually got enough money together for a HDTV.
A HDTV is better, but a monitor is still a more than viable solution, make sure it supports HDCP though or else the PS3 won't display a HD picture.
[EDIT] Just to add to Knives' post, HDCP is possible via a DVI->HDMI adapter as long as your monitor supports it so if your monitor only has DVI all is not lost if the monitor supports HDCP.