Hi Christian
The performance activity won't be part of the course as such but you can generate a performance activity for an audience that contains an audience rule that they are enrolled in the course.
The performance activity can be closed on a due date or on completion
There are various settings that control who can participate , respond and view responses and when the activity sections are closed
Notifications for reminding users to complete the performance activity can also be setup
Theoretically you could have a label activity in the course that is just a link to performance activity but the problem is that the activity completion isn't linked to the performance activity completion and the link would be different for each user.
Regards