Do mods actually have the power to deprive the user of the usual notification by PM?
Yes.
No.
ON another SMF forum there is a post:
As a global moderator I click delete and get this dialogue box:
I click ok, and the message is gone.
It's absolutely the same here.
[edit] and a message is automatically sent to the user of the deleted post.[/edit]
No advice to the user.
Mods do not have the option to disable notifications that a post has been deleted.
Hilarious has already given the case where you will not receive a notification for a deleted post.