Registering on client directly sounds good. I remember reading on your page though saying it would disable normal login/registration on the WordPress site though. I was just suggesting that you had a way to tell WordPress to associate your WordPress account with your intersect account afterwards for sites that are already established. Similar in a way you can connect your socials on sites.
Example, I have about 120 accounts on my WordPress site. According to what you have at https://intersect-connect.tk/intersect-management-wordpress-plugin/ you are saying default WordPress login/registration should be off.
By making the system where users can tell the plugin what their account is and then verify it, it would allow the default functionality of WordPress. Otherwise you're asking users who have established WP sites to stop their normal operation. And by that point, it's an easier decision for most to probably just install the CMS and get the shop functionality that way.