Notifications are sent based on the Sessions not the Events so if all your events are in a single session, they would only get 1 email (user enrolled in ILT session template)

I get 1 email per event, not per session. I did a test run with 3 days and it gave me 3 notifications for all 3 days, under the single session.

That’s odd...I just tried it again with the template, User enrolled in ILT Session and got 1 email with all 3 events listed + I calendar attachment that added all 3 events to my calendar...If it’s not working this way for you perhaps reach out to support to ask.

I am not sure if the Connector can be turned off for specific courses, but ​@lrnlab is correct.  If you use the platform notification with the event User enrolled into ILT session, the user will receive one email for the entire session, with the listing of all events and the calendar attachment. 

We usually include instructions in our notification about how users can open the attachment and add them to our calendars. 

Yes you can selectively turn OFF the use of Connect at the course and/or session level; if that is the source of your issue.