Yes you're right, the forum is notified when there is a new message unread.
But for the first time, when the forum is empty, there is no notification in the course overview block.
For exemple, the forum is empty, no message :
We can see only the assignment activity but not the forum activity
When someone posted a message, there is the notification into the block, yes
You said : "So far I couldn't figure out how to make a discussion forum appear in the course overview block. When students log into the DE site, they can see assignments and quizzes, if they need their attention in that particular week, but no discussion forums"
So I thought it was in case of the forum is empty for the first time, as a to do list...
To be simplier, you can put the first message into this forum to give description of the task, without using assignement workaround...