If your AVIs are DV-AVIs -- the kind created when you capture over a FireWire connection from a miniDV camcorder -- they will work just fine in Premiere Elements Mac. In fact, they work at least as well as DV-MOVs.
As John points out, you may not be able to play a DV-AVI in the Mac's Finder. But, if you've properly set up your Premiere Elements project for DV video, they will work just perfectly in your Premiere Elements project.
I'm curious how you got AVIs as your captured footage, by the way. Did you capture your video on a PC and then transfer it to your Mac for editing? (The Mac version of Premiere Elements captures DV video as DV-MOVs.)