Is a user automatically part of a group of the same name?
No. Unless the user's group is set to _example (in the password file) or the user is explicitly added to the _example group in /etc/group, the user is not a member of that group.
Users must be explicitly added to any group. It is common convention to have a group for named the same as each user. The operable theory is that other users may be added to a particular user's group in an adhoc fashion allowing the user to control which files are exposed to that group.