I'm able to run Shine in Final Cut Pro 5.0.4 but not in 5.1.2. I've tried it on both a G5 and an Intel-based Mac Pro.
On the Mac Pro it doesn't seem to know it even exists. Perhaps that is a universal-binary issue.
On the G5 it does seem to "see" it but I get the error "AE Effects Error: Unable to find the plugin 'Shine'. Do you wish to load plugin from another directory?"
Clicking "No" doesn't help and clicking "Yes" and guiding it to either the Library > Application Support > Final Cut Pro System Support > Plugins > Trapcode or to the Adobe After Effects 7.0 > Plug-ins > Trapcode directories doesn't help either.