It is the RAM which matters most in your case, not the processor. I run Fedora on Celeron 366 MHz machine with 512 MB of RAM.That's weird. I run Fedora on a P3 800 with 768MB RAM and a Radeon 7000. Everything runs great. P4 should definitely be fine, I would imagine.
It works fine .. obviousely on Desktop compi.
-mandar