Actually, no. The cook has to cook. Restaurants don’t hire more people than they need to stay in business while serving the customers. If only the government operated the same way.
That is how fedgov defines essential, though. Essential does not mean redundant.
Essential means that the position is necessary to keep the infrastructure necessary and to prevent possible damage to property or lives.
I'm DOD though, and as someone else pointed out, we are already funded so it doesn't affect me. In a shutdown my command will have a skeleton crew of first responders and people necessary to maintain plant equipment in a safe condition. That's it. If something else comes up and they are not involved in an essential function, they do the other jobs.
As far as back pay goes, I have learned to always volunteer to be the guy furloughed. Chances are the funding legislation that eventually passes will include back pay...not always, but usually.