Allow public users to sign up to the identity provider?

I'm currently looking into the possibilities that SSO may offer but wondered if this was a possible use case:

Let's say you have a public website, accessible by users (members of the public not employees) where they can sign up to the website, but instead of signing up to the website, the user is signing up to the IdP instead where they can use SSO as a form of login to the website. Is there any way to do this? This would also mean that the user is able to access different applications that the company may authorize.