Hello,
s2Member works on and from the domain where the plugin is loaded. If you have a blog farm with multiple sites, s2Member would run independently on each of the domains. If a user purchases something through s2Member running on child.domain.com, then the user would be registered and authenticated only on child.domain.com, not on domain.com.
Here is some more information about how s2Member works with Multisite:
While s2Member is compatible with WordPress Multisite Networking, the sites within a WordPress network are separate and not interconnected. That means you cannot share users, logins, or other data across the sites (including access control).
Please see the following from WordPress.org:
The sites in a multisite network are separate, very like the separate blogs at WordPress.com. They are not interconnected like things in other kinds of networks (even though plugins can create various kinds of interconnections between the sites). If you plan on creating sites that are strongly interconnected, that share data, or share users, then a multisite network might not be the best solution.
The s2Member Multisite feature allows you to offer the s2Member plugin to sub-sites, giving your sub-sites the ability to setup and use s2Member on their own. When you upgrade s2Member on the primary site, the s2Member plugin is automatically updated for all your sub-sites. However, things like access restrictions on one WP installation are not shared across WP installations (again, the WordPress Multisite feature itself isn’t designed to work like that).
There are plugins that allow you to get around these WordPress Multisite limitations, however they may or may not work with s2Member.