Unlikely to do it unless the avi is using all mp4 codecs and just needs repackaging.
MPEGStreamclip is possible. Try "save as" and see if it works. If not you may be able to get by with just converting one of the components and passing through the other if it is a mp4 variant.
Use Media Info - http://mediainfo.sourceforge.net - to get details of codecs used in multimedia.
Many AVIs use mp3 as an audio codec so that one at least will need converting.
If you end up having to convert, some use Handbrake.