If you use Automatic Duck on your end, you should be able to read the clips. There is an option to read the original Avid media when you import the project.
Automatic Duck will only read your timelines and create QT media clips of Master Clips edited into that sequence. Auto Duck will not read all the Master Clips that is within the whole Avid project. You could, however, get these clips across using Sebsky Tools (www.dharmafilm.com/sebskytools).
All in all, you COULD export all Master Clips from Avid as QuickTime files in a codec FCP can handle, and then add TC using Sebsky Tools – then export all sequences from Avid using Automatic Duck and finally reconnect the imported sequence to the qtfiles. However, given FCPs way of mediahandling, you get into trouble if subclips are used. And if clipnames are more than 31 characters, etc. etc. Also keep in mind that a lot of visual effects would have to be rebuild.
Going the other way, relinking imported sequences in Avid to existing media is a lot more stable.
I have digitized on Avid and transfered the media to FCP for editing on quite a few projects, and while it is possible, there are a lot of things that can go wrong, so unless you have a very compelling reason to do it, I would suggest that one of you change software.
All the best,
Peter