The last ‘topic closed’ admin log on my test site is from 4 days ago. The two I’ve just been playing with with the Timers do not show up there. I will investigate further. 
Update:
I’ve just run it again, and if I set an Auto-Close timer for 1 minute after the last reply, the topic closes but no admin log is created. 
The only related thing in there is the record of the category settings change to add the timer (when I add one through the topic wrench, it leaves no record).
By the look of it, the only place to find a record of a topic timer (other than the close message itself) is through using the Data Explorer and checking the topic_timers table.