Should'nt be any problem. I'm running FCS 2 on Tiger here.
Here are the actual specs
Minimum Requirements to Install All Final Cut Studio Applications
* A Macintosh computer with a 1.25GHz or faster PowerPC G4, PowerPC G5, Intel Core Duo, or Intel Xeon processor
* 1GB of RAM
* An AGP or PCI Express Quartz Extreme graphics card (Final Cut Studio is not compatible with integrated Intel graphics processors)
* A display with 1024-by-768 resolution or higher
* Mac OS X v10.4.11 or Mac OS X v10.5.5 or later
* QuickTime 7.5.5 or later
* A DVD drive for installation