- The functionality of the plugin should only be applied on the level of creating new sites.
Sorry, I'm not exactly sure what you mean by this. I think you mean that you ONLY want new Members to be able to create new sites, and that's it. If that's the question, then yes. You would just bring in new Members on the Main Site of your Network, and after registration, allow them to create a new Blog(s).
- The site-owners won't have any access to manage memberships to their visitors.
Yes, when you enable s2Member, do NOT enable it "Network Wide", just enable it on the Main Site of your Network, and that's it.
- Upon registration I want the site-owner to be assigned another (custom) role than administrator
Sorry. That's not something that s2Member deals with. The default WordPress behavior is to make a new site owner an Administrator of their new Blog. You might find another plugin at WordPress.org that could help with this though.