WooCommerce and s2Member

Yes, it would.

Does Role-O-Tatic store its own database of users? And what happens to all of the existing members who signed up through s2Member?

Nothing happens to existing members. All RoM is doing is creating another way of giving people s2Member roles.

New members created by RoM are WooCommerce customers, and their details are stored accordingly. If you want more details, ask the RoM developers themselves.