it might be possible to make it log when it's complete...What i would do, if i were you is this:
Go to the project page as googlecode and add a feature request. Request that the unpack plugin has an option to enable logging on auto-archive to the "logger" tab
Right now novik is REALLY busy with paid work but when he's able, if he thinks it is a sane request (and if it's possible) he will add it.
It sounds reasonable to me, and it should be fairly simple because when you call unrar via shell it has an exit code which you can use in scripts to know:
unrar completed
unrar has stopped with an error
but like i said, you need to actualy request this feature, or perhaps open a bounty.