I actually found a solution to this problem with .GIFs.. After you have a .GIF saved onto your computer, you can find a site like this one (that I used): http://www.online-convert.com which allows you to insert your .GIF file into the video option and convert it to .mov. It's quite convenient, so that .mov files can easily import to Final Cut Pro X.
I created a tutorial explaining how I do this. It runs through how to capture a gif and set it up for editing in Final Cut Pro X.
The video is pretty quick and to the point. Hope you find it helpful.
Here are a couple more tutorials I created about working with animated GIFs that you might find useful:
Final Cut Pro X: Import an Animated GIF with Transparency
Final Cut Pro: Create an Animated GIF from a Video and Upload it to Twitter
Let me know if you have any other FCPX questions.