In short, yes, they still can.
Workers Compensation is offered on a no-fault basis, meaning that the employee doesn’t need to prove that any negligence occurred on the part of the employer. Once an employee accepts compensation under Workers Compensation, the worker also gives up the right to sue the employer.
However, if the loss is not covered under Workers Compensation or the worker does not agree to the compensation offered under Workers Compensation, then the injured worker can sue the employer to recover any damages incurred. Employers should consider purchasing Commercial Liability Insurance to provide coverage for such cases.
See An Intro to Workers’ Compensation to learn more.