When I receive an email in thunderbird I know I won't read (an advertisement for instance), that should be useful to delete this mail directly from the notification that appears on top of the screen (see this screenshot showing such a notification)
I'm returning to Thunderbird after many years' absence and I'm impressed with all the improvements and how good it looks and functions. My immediate reason for returning was the fact that Comcast Webmail did not support sound notification or any notifications, for that matter.
So, yes, after quickly getting used to the presence and value of notifications, I would definitely support the addition a "delete" option to the popup notification.