Once a new students signs up to your course (free or paid) they can be added to your Convertkit account.

In Convertkit, navigate to Automations > Rules > Add Rule

From here you can select the Trigger: "Purchase a product" and the Action : "Subscribe to a sequence" and/or "Add a tag"

You can enter the new students into an automation based on which tag you add to them.

Note:

How to add Teachable Students to Convertkit