Maybe!!!
The argument often made for the HDMI signal format is the "pure digital" argument--that by taking a digital recording, such as a DVD or a digital satellite signal, and rendering it straight into digital form as an HDMI signal, and then delivering that digital signal straight to the display, there is a sort of a perfect no-loss-and-no-alteration-of-information signal chain. If the display itself is a native digital display (e.g. an LCD or Plasma display), the argument goes, the signal never has to undergo digital-to-analog conversion and therefore is less altered along the way.
But the fact is depending on the type of media you put into your PS3 (eg blue ray, or avi off a usb) even digital conversion from digital to digital might be needed.
I only say yes because I just got a PS3 and switched from component to HDMI and the difference is a little crisper of a quality photo.
The only way to really know is to try and if the cost of HDMI cables is deterring you, just go on ebay and you can pick one up for $15.
Congrats on the PS3 btw...it is a great system. If you watch a lot of movies off your computer or have a lot downloaded I would suggest you get TVersity (free program that lets you stream content right off your computer onto your PS3...no more usb or converting the video!!)