An employer can Google current employees. The only thing that the employer will want to be careful of is if it finds information that it is going to rely on in the Google search to terminate them they want to make sure that they are permitted to rely upon that information as a basis for terminating that employee.

If the company sees that the employee is complaining about unsatisfactory working conditions, if they try to fire them for that reason then that may be something that’s protected under the National Labor Relations Act, and they could be held liable if they rely upon that reason for terminating them.