Yes, you should be able to as long as your video supports HDMI out such as the ATI Radeon HD series. For ATI Radeon, just make sure you have the latest Catalyst Suit installed that your card will support. You'll need to use the DVI to HDMI adapter which came with your video card. If you don't have one, you can pick one almost anywhere these days.
If you have some other card such as nVidia or otherwise, I would have to advise you to look up the user manual from the manufacturer to find out.
As for sound, you can either use the HDMI (sound through the TV) or sound through your system. You just need to right click on the speaker icon in the system tray, select playback devices and select the playback device you want to use for sound.
With my current setup, I have one of my outputs connected to my Sony Bravia TV and it works great.
I run Windows Media Center to watch Internet TV and NetFlix or when I'm not doing that, I use my browser to watch Hulu.com FUNimation.com or other websites where you can watch streaming TV shows.
I still have one of my 24" monitors connected as my default desktop and next year I am planing to replace my HD4850 with a 5870 or a 5890 so I can run both my 24" monitors and my TV.