Aperture relies heavily on the graphic card, so if your G4 has enough RAM and one of the graphic cards listed on Apple's Aperture page (here
) then it should run (but not fly). I doubt that you'll be happy with the performances, though. A G5 tower with good graphic card or a new Mac with Intel chips is the way to go.
The demo version is free, so download it and try it.
Aperture does a hardware check and will refuse to install on a G4 desktop machine. There are workarounds to this ("hacks") on the web, but my practial recommendation is to get new hardware (Aperture really does run best on Intel hardware) if you want to give it a real shake.