If you use a version of iMovie that was designed for the G4, and you are editing SD video such as miniDV, you should be fine. Video editing was certainly possible with the G3 iMacs and the G3 PowerBooks that CNN handed out to field reporters, so it's possible with a G4. But you must limit yourself to SD and low-res webcam stuff.
The problem is that the G4 won't run today's iMovie very well, and cannot play back, or edit, HD video at all.
The G4 can easily play back the not-very-compressed QuickTime movies of its day, and of course it can also play DVD movies like the G3 could. But again, you'll never see a G4 play an Blu-ray or HD YouTube video because it just doesn't have the power.