Does workers' comp apply to workers paid in cash?
Usually, yes. In most states, whether someone is an employee for workers' comp turns on the work, not on how the person is paid. Someone working under the restaurant's direction, on its schedule, serving its food or pouring its drinks, is generally an employee whether or not the wages were reported. If that person is hurt, the claim comes to the restaurant, and the premium audit can add the unreported wages to the payroll the premium is charged on.
What decides it
The tests vary by state, and they ask the same kind of question: who controls the work. Who sets the hours, who supplies the equipment, who tells the person what to do and how. A friend paid to run a delivery, a server picked up for one event, a bartender paid at the end of the night: if the restaurant directs the work, the restaurant is generally the employer.
A true independent contractor runs a business of their own. A bartending company or staffing agency that sends its own people, carries its own workers' comp and can show a certificate for it is a different arrangement, and the certificate is the thing to ask for.
If the person is hurt
An injury on the job is a workers' comp claim wherever it happens, at the restaurant or at a client's event, and the restaurant's policy is the one it comes to. Paying in cash does not move the claim anywhere else. It only means the person was never on the payroll the policy was priced on.
At the premium audit
After the policy year ends, the carrier's auditor reconciles the estimated payroll with the real one. Auditors ask about cash payments, 1099s and casual labor, and payments to people who had no workers' comp of their own can be added to the payroll the premium is charged on. The help that was never on the books shows up on the audit bill. More on how that bill is built: Why did my restaurant get a premium audit bill?
The simple rule
Anyone who works a shift for the restaurant goes on payroll for that shift, even one night. It costs the payroll taxes and the workers' comp premium on one night's wages. The other route is a staffing agency or event company with its own coverage, with its certificate on file before the event: What your certificate of insurance actually proves.
December is when this comes up most, with the busiest nights and the most one-time help. The same holds outside the four walls: an employee driving an order in a personal car raises its own question, Does a restaurant need hired and non-owned auto?