While I don't think there is any support specifically for auto-shutdown, if the completion of a torrent download triggers that auto-shutdown, that can be logged. But tixati did recently add support for performing shell commands based on several events.
http://support.tixati.com/file%20completion%20shell%20commands
I think you might be able use the xfer: along with a write command to append some comments to a text log file for example.
as of v2.33, more variables are provided:
"file completion shell commands support additional placeholders $path $basepath $name $ext"
see the folks in tixati channel
Scripts Я Us and they might have more ideas for you.