Yes, it is possible. If the old external iSight you have still works, it should work with the new Mac mini. You can test an external iSight using the suggestions in this link.
To try an external (Firewire 400) iSight with a FW800 mini, you will need a Firewire 400-800 cable or adapter to connect the FW400 external iSight. If you don't already have such, Apple currently offers this adapter: http://store.apple.com/us/product/TW748LL/A/
If you have problems, I'd recommend a new compatible USB cam that offers a current manufacturer's warranty instead of any external iSight. Some examples of current compatible cams are described at http://www.mac-compatible-web-cam.com/
If you want to read more, start at http://discussions.apple.com/thread/3983993 (BTW, current FaceTime versions work with external iSight's mic.)