No. A shut down is a shut down. In the real world a shut down means don't come to work and don't expect a pay check. Government workers are not a special class of workers only first responders should not be allowed to strike or get caught in a shut down.
All of a sudden everybody is worried about government workers. In my opinion they may be overpaid, have in realistic benefits ( generally at no cost to them), unbelievable retirement programs and you can not easily fire them. They used to be considered underpaid but that is no longer true.