As it currently stands in Version 4.7.11 Beta 2, once you click on the check mark shown below the deletion process is executed, and no trace of the action is logged.

I suggest that upon clicking on the check mark the request is moved to a new section called "Deletion Requests Completed" with the photo and email redacted as they would be considered PII.  But the deletion request and the day it is completed should be logged for auditing purposes.

This way you could detail later that a member by the name of "X" who joined on a particular date was ultimately deleted "per request" on another particular date.

Administrator actions are logged (like for everything else too) in the Administrator Logs section (I did just fix a couple language strings)

@Stuart Silvester Thanks for letting me know account deletions are being logged in the Administrator Logs. I never thought to look there.

I noticed an anomaly in the Administrator Logs:

Deleted member: Member 4 #9

Not sure what the "#9" stands for.  Could you please elaborate on its significance?

 

That would be the ID