Hi,
No, it doesn't require a shipping address.
It just require that you display the address fields on the registration form (these fields will be added as the address of the user, and will be used for either the billing address or the shipping address, so even without shipping, the system will still use them for the billing address).
So you need to have the "ask address on registration" option of the configuration turned on, and you need to have the address fields firstname, lastname activated and set to display on the frontend via the menu Display>Custom fields.
You actually don't need to ask the full address if you don't want.