This reminder is sent to a user with an EOT time set for his account. This happens when a buy now with a time limit is purchased, or when a subscription is ended, i.e. you know the time the paid access ends. It doesn't apply to an ongoing subscription, since that will not set the EOT time before it's stopped.
The Reminder Emails feature status would be the default for all users, and the profile setting would override the default for that user. If the default is on, but the user's is off, he won't receive them. If the default is off, and the user's is on, he wouldn't receive them, because the reminders system is not active. In the profile's setting, if you click the (?) link, you get a message saying:
This setting applies only if you have configured reminder email notifications in s2Member; e.g., EOT Renewal/Reminder Emails or NPT Renewal/Reminder Emails.
I know it's a bit confusing. I'll look at this some day in the future, to try polish it and make it more intuitive.
So, to recap: If you have the Reminder Emails system disabled, I doubt your users will get them, even if set to yes in their profiles, especially if you delete all the dates for the reminders and the reminder email's subject and message, just to be extra safe. But if you want to have all users set to no in their profiles, then you'll need to add a row for each one in the usermeta table with that value.
Does that help?