Typically, yes, as some options, such as an ESOP, are required by regulation (ERISA) to be broad-based qualified retirement plans. This should not be confused with 100% of the company being owned by employees, but rather 100% of employees participating in the ESOP.
For worker co-ops, there is typically a probationary period before which a new hire has the opportunity to apply to become a worker-owner, and to begin to pay (or all at once pay) an initial equity contribution, and some employees may elect to never apply to membership. However, worker co-ops are still considered broad-based because every employee who meets the required criteria should be able to decide if they wish to apply for ownership.
In an EOT, like an ESOP, the trustee is a fiduciary agent on behalf of all employees.