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I only watched about the first 45 seconds. Based on that, I'd say it's feasible to do in Final Cut. It was fairly basic animation.

But you'd save yourself a lot of headache and time by using a motion graphics program like AE or Motion.
 
That was likely made in After Effects, but you can do something similar in Final Cut, not sure about iMovie though. It's just a bunch of elements keyframed about.
 
Either AE or Flash(?).
To do this in FCP is going to take forever and will never come out as smooth as this.
 
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