The best information I have been able to locate for this is in an older support forum for S2 Member:
The question that was asked is the same: How can S2 Member ensure that a person has subscribed to an email list before access is granted to the website?
The answer given is:
(1) Automatically subscribe the user to the email list through an S2 Member hack (in the thread). This disables the MailChimp confirmation email and places the user directly onto the list.
(2) Maintain the double opt-in required by MailChimp for their lists (which is also good practice, generally) by having S2 Member send a confirmation email with a temporary password to the user. The user must then login to the site using the password that was emailed. As long as the site has this (or some other form of) double opt-in, then MailChimp permits the hack above which causes their list double opt-in to be disabled.
(3) It is also possible to configure a required checkbox in S2 Member, which states that the user agrees to receive email from your site. (This seems like a good idea, both from a transparency standpoint, and also to remind your new user to expect email from you.)
Step #1 above guarantees that the user is subscribed to your list before they can access your site. But I'm not sure that it really qualifies as double opt-in. It appears as though a user would be automatically subscribed to your list even if they never opened the confirmation email sent by S2 member.
Perhaps it would be wise, then, for the first email in your autoresponder sequence to remind the user what they signed up for, and how to login.
I am currently researching this same issue for my own site and this is the best information I have been able to find so far. But perhaps the S2 Member support team will respond with more up-to-date information. As a purchaser of the "Pro" form of the plugin, I have found them to be very helpful.