In a word - YES. 

There is nothing in Federal Acquisition Regulations (including the DoD Supplement) , Manpower utilization Regulations or Instructions (e.g. DoDI 1100.22), and law that prevents contractor personal from being categorized as "emergency essential" personnel. In fact many contracts require this depending on the services being provided in a GOCO (government owned contractor operator facility).

All of that said, normally these personnel know they are designated as such as terms of their employment with their company BEFORE such a situation arises.

If that is not the case then I suggest you discuss this with your HR specialist.