Back to the original question... yes it would run FCE. But editors would recommend a MacBook Pro for the horsepower, and, of course, the Firewire port.
for a little less money you can get a faster MacBook Pro with faster processor, a much bigger hard drive, built in DVD (vs. a USB Tag along DVD), a bigger screen and a lot more plug in options (more USB ports, Firewire 400 & 800, Ethernet, DVI, etc...).
(Price compared with 1.8GHz Proc, and USB DVD added to MBA and FCE added to both.)
I'm sure I missed something, but other than the size/weight of the MBA, I would go with a MBP. (picks up phone to call Apple...)