Yes. Users with Create Task privileges can assign Tasks to existing third-party contact users. 

The Tasks assignee field will search master data for all active internal users and active third-party contact users. To facilitate task completion, third-party contact users will have access to a Tasks tab on the third-party Gateway landing page, where they can view and complete assigned tasks. 

Note: the third-party user must have been assigned a DDQ and must have logged into the system to view their Tasks table.

When assigning a task to a third-party contact, the system will notify the submitter to confirm that the Task is intended for an assignee outside of the submitter's organization.