It's possible - but it often wont work.
Here are the facts:
Video cables need to be made with something called "75 ohm" coax. The Yellow cable in a set is made with this and often the red & white cables are also identical.
But people got wise to this and places like Radio Shack started making the red & white cables with different coax which work for audio, but mess up the video.
ALSO - component cables are not HD cables
Component has been around since the 1940's. If the package says "component" - it only has to work with standard def video which has a max frequency about 4 mhz.
Progressive video goes up to 12 mhz
HD video goes up to 35 mhz
Lots of "Joe-six-packs" buy a $10 component cable from the dollar store to hook up to their new HDTV and then brag how they saved money. They don't know enough (or don't admit) how there is a loss of fine focus details, some ghosting, colors are not solid, etc. (The jump in picture quality over standard def is amazing so this hides the flaws).
You can get good, HD video rated cables from www.bluejeanscables.com for about $50. These will perform as well as the $200 Monster retail cable and they have published frequency response and other specs that video engineers look for when used in the broadcast industry.
There IS a lot of fraud/junk science going around to get you to over buy on cables. But dont be super-cheep and try to use old yellow/red/white cables on your new HDTV - buy the proper cables.