It will work, but as mentioned you will definitely want to upgrade your RAM - there are many 13" white Macbooks that are in your CPU range, you will want to confirm your version but if you have a relatively new one you should be able to upgrade it to at least 4 gigs - I have edited with 2 gigs, 4 gigs is much nicer when editing video. One concern is if you have an Intel GMA X3100 or 950 - some fxplug features may not work - but that may not be critical to what you do (most features of the software will work fine - not even Apple was able to tell me back when I was shopping for a Mac which filters wouldn't work on the GMA chipset).
As you probably already guessed, you will not want to use your internal drive as your scratch/media drive. You will want and external Firewire drive (not USB if possible - although USB will work, it's much slower then firewire when dealing with large streaming files similar to video files) to act as your scratch/media drive. You will then need to go into the settings within FCE and tell it where the scratch/render/media drive is and it should use that to store your video/audio.