Testing in the current dev release Moodle 4.0 we've seen the following behavior:

• Teachers cannot submit assignments (expected)
• Site administrators cannot submit assignments (expected)
• Site administrators who are enrolled in a course can submit assignments (unexpected)

This last appears to be a change from Moodle 3.11. It manifests in at least two places:

• The user sees the "Add submission" button on the assignment page
• The timeline block lists the assignment for the user, and shows overdue notifications