You. probably want to use Groups to capture these users and then use Enrolment Rules to assign the standalone ILT course. Keep in mind that groups can only recognize course status so you’ll need to choose 1 course in your LP as the trigger. You can have set to any status (doesn't need to be a completed course). Also note the user will still need to register for an actual session as the automatic rule will only enrol them into the course, not the scheduled session(s).

Our students are not allowed to self enroll so if they are automatically enrolled into the standalone ITL course, this automation will not enroll them into any of the sessions?

Correct...there is no mechanism to automatically register a user for a scheduled session; only for courses. You can do this as an admin, whether a power user or super admin however if you choose this route, you wont need any groups or enrolment rules.