Right now, personal Google accounts can join existing classes in Google Classroom. In the upcoming weeks they’ll also be able to create classes. I tested Google Classroom with my personal account, and could join classes but not create them. My G Suite for Work account couldn’t join or create classes, but I was given the option to express interest in that ability.
For G Suite for Education admins, there are new options in the Admin dashboard for Google Classroom on controlling what accounts can and cannot join and create classes in Google Classroom.