Let's face facts:
The requirements for Final Cut Pro are:
Macintosh computer with a 300-MHz or faster PowerPC G3 or G4 processor and built-in FireWire
500-MHz or faster single or 450-MHz dual processor Power Mac G4 or PowerBook G4 required for G4 realtime effects
667-MHz PowerBook G4 required for mobile G4 realtime effects in DV format
Mac OS 9.2.2 or Mac OS X v10.1.1
QuickTime (included)
256MB of RAM (384MB recommended for G4 realtime effects)
40MB of available disk space required for installation
From Apple's Final Cut pro
site.
Now obviously, if Final Cut Pro 3 will run on a Power Mac G3 at 300 MHz with 256 MB RAM on OS 9.2, then it will surely run fine on a 1GHz 17-inch iMac.
Final Cut Pro will even work on the white G3 iBook.
Disk speed is a factor limited only to iBooks and PowerBooks; and, of course, older Power Mac G3 platinum towers. Generally a 5,400 RPM drive or faster is sufficient for DV capture and editing. The new 17-inch iMac has a 7,200 RPM drive.
The question is not whether the application will work okay -- it will work fine...but how long do you want to wait for the rendering? Keys, intensive wipes and DVE work will require extensive rendering.
Additonally, as has been mentioned, DV consumes a lot of drive space and you're likely better served by a PowerMac. Even if you can only afford the new 1GHz Power Mac model, you would later be able to add more hard drives and even add other capabilities to which the iMac limits you.
If you're doing this for casual editing sort of a hobby for home videos, get the imac and Final Cut Express. If you're going to use the system to break-in to the video biz...get the iMac and full-blown version of Final Cut. But! if you're doing this professionally, get the PowerMac and try to get the dual model if possible.