It depends on your monitor, but that's exactly what I did for a year or two. My monitor allowed me to select input between DVI and HDMI, and I ran my PS3 to my HDMI, with PS3 sound running out through component to my speakers via an adapter.
Most monitors with multiple inputs should let you choose your input, especially if one of those inputs is HDMI. --- "How do I get rid of a Trojan Horse?" -Sailor_Kakashi "Leave it outside the gates of Troy overnight." -Davel23
Depends on your monitor. I have an HP x2301 and it has an input switch button so I can switch between VGA, HDMI, and DVI on the fly (even when they're all in use). If you're only using one or the other at a time, then your monitor will autodetect the correct input.