Hey dudeabides.  Welcome to macmod.

Final Cut Studio's current version needs at least a G4 1.25GHz but with a dual 800 you just might be able to get it to run.  Keep in mind though that the newest version won't be fast at all on your system.

The main issue I see you having is at the install.  Most apps (even if then support dual CPU) don't see a combined power of 2.  They look at the speed of the cpu whether its 1 or 2.  My feeling is that it will see an 800MHz and not install.  Apple is known for putting MHz verification in the pro app installs.

Worst case is remove the hard drive and put it in a mac with a 1.25+ G4 and then install.  This is assuming there is another mac you have access to through a friend etc. 
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Mac mini C2D 1.83GHz - 2GB RAM - 200GB 7200rpm HD
Sawtooth w/G4 1GHz - 1GB RAM - SIIG SATA w/2x1TB HD
B&W w/G4 600MHz - 1GB RAM - 2x80GB HD
Sawtooth G4 400MHz - 512MB RAM - 40GB HD
Dell Ultrasharp 2007WFP 20" Widescreen LCD
2.94TB Total Storage