Yes, assigned tasks are automatically created and recorded in the Assigned Tasks area of the Sponsorship page when there is a transaction connected to a sponsorship such as a gift or event level purchase. If the Sponsorship Gift button is marked YES on a gift and a Sponsorship Level is selected, all of the tasks that are associated with the sponsorship level are linked to the constituent and can be seen on the Fundraising > Sponsorships > Manage Follow Ups page. Sponsorships can also be linked to event and membership levels.
There is also a new feature where those assigned tasks can create Follow-ups for DonorView users. To learn more about this feature, see this article https://support.donorview.com/en/support/solutions/articles/9000217093-how-do-i-assign-tasks-for-sponsorship-follow-ups