WooCommerce REST API Capability

I have a main site with WooCommerce on it. I have a custom plugin (Remote Sites) that I want to have people register and purchase free product (No credit card) on. Is this possible via WooCommerce REST API?

The flow would be like this: People find my plugin in the WP repoz. They download it and install it. They activate it and go to the admin of it. They see they need an account. They click “Register” and the form pops up and they register just like the checkout form on the main site. The “Free” product is already selected then they click “Complete Registration”. It will create the account and the order on the main site as normal. I just need to do this remotely via the plugin and hope that the WooCommerce REST API can do this.

Thoughts?