First thing to check is the dmesg output after you boot up,
look for ivtv and v4l loading. If this was successful you will have a /dev/videoX device, which you can check by doing an
ls -l /dev/video*
It will most likely show up as /dev/video0. If you see all this info, and Sarah does not pick it up, you may have to run mythtv-setup manually to get the card configured for TV viewing/recording.
You can get to mythtv-setup from the Advanced>Computing menu option on the UI for LMCE. It looks as though that chipset is supported by the kernel. also, in searching to see what a Falcon II tuner was I stumbled across this link in ubuntu forums. Looks like they are using this very card:http://ubuntuforums.org/showthread.php?t=859090
Best of luck to you. And if you get it working, don't forget to add it to the wiki, for future use by yourself and others. The wiki is your friend