It should work fine, I ran FCP 4.5 on an iMac G5 1.8GHz Rev. A and it worked well. It will not be as fast as a new iMac but it'll get the job done.
Can I ask what type of work you'll be doing on FCP and what version you plan on using?
I have ran FCP on a 17" 1.5 G4 Powerbook. Not the way I would want to earn a living, but it worked well enough to do editing. You will obviously take a hit when compressing and rendering. Overall, it will work well enough to produce a fine product.
Works just fine no worries, storage becomes a problem. You can't add additional hard drives internally, you have to get external firewire hard drives if you need more space.