AVI is not a codec, just a wrapper. FCP works best when it has a quicktime wrapper so firstly the AVI needs to be converted to a quicktime and also you may need to transcode the codec to something that editis nicely in FCP.
I have in the past dropped an AVI animation codec file into an FCP timeline (final animated graphics file) and just let FCP render it as I was onlining and adding a late change before playing out to tape.
If you are editing then it would be smarter to convert to a quicktime to avoid endless rendering everytime you change an AVI clip
I work with avi files all the time - you can import them without a problem. I have found that they exhibit weird behavior sometimes, like getting out of sync, so I usually render them to a mov first, then import.