no, you'll need one with a proper graphics card, not the intel chipset. it kind of takes away the point of using the mac mini with final cut pro really.. it's a pro app designed for high-end equipment, certainly not the mac mini.
the iMac will run it fine, however. ideally with 2GB RAM and the best graphics card it can come with. or an older powermac G5, though sometime in the next few months, an intel version of the powermac should be released.